If you're new to the world of electronics, let me be the first to welcome you. There are many good resources available to help you get started. For a list of recommended resources, see step 4. But once you find the right project, how do you bring it into reality? Of course you will need some electronic bits to make it work, but I'm talking about making it. Building it and using it in a real life project. What tools do you need to be successful? Well, hopefully I can help you with that.
I'll break the list down into three parts, Basic, Advanced and More Advanced. The links for everything except for the Digilent Analog Discovery and Electronics Explorer Board are just to illustrate the item and are in no way an endorsement of the item or the seller. Some of them are the exact item I have and use, others I don't even have myself, it was suggested that they be added to the list. Purchase your tools at your own risk. I do recommend you spend the money you have on quality where it counts. I also highly recommend you purchase either the Discovery or the EE board.
Step 1: Basic Tools
Mostly hand tools and small stuff, in no particular order
+ breadboard - it is absolutely critical that you prototype your projects before you start building and soldering. Breadboards are the way to do that. Don't say I didn't warn you. I have several small ones like in the link and then connect them together as I need more space.
+ jumper wires- for making connections on the breadboard. I prefer the type in the link, but this type can be useful as well, especially the smaller bits that are great for short distance connections.
+ spools of wire - different wires for different uses. 16-22 gauge, both solid core and stranded.
+ soldering iron - I use a 40W iron for nearly everything. That being said, an adjustable iron is probably better as it will give a wide range of temperatures. Parts are not immune to heat, so a higher temperature or smaller part will require less time to solder and avoid damaging the part. An iron that can use assortment of tips isn't a bad idea either (see this Instructable for a great guide on different soldering tips). If you want to learn to solder, check out the coolest how-to-solder videos I've ever seen!
+ solder and flux- I use a larger diameter (.050"; 1.27mm) solder for soldering large bits and smaller diameter (0.032"; 0.81mm) for smaller connections. You don't want to flood a small contact with the large stuff or use up your whole spool of small stuff on a large contact. I use solder with a rosin core, which is just built in flux. Solder also comes in different ratings based on the ratio of metals it's made of. I use a 60/40 solder (60% tin/40% lead) for nearly everything. Silver-bearing solder has silver mixed in and is better for joints where a high frequency signal will be used as it is more conductive. Flux can be either liquid or paste. It's great for cleaning the oxidation off the joint as you heat it up right before you apply solder. It can be used whether your solder has a rosin core or not.
+ solder wick and vacuum - for desoldering parts when you mess up. I use both, the vacuum for large amounts and the wick (a.k.a. desolder braid) for small quantities. You can also get an all-in-one desoldering iron with a vacuum bulb attached. I personally don't like it. I think it is too difficult to manage the bulb and iron in the same hand, but I'bler bergerab loves his.
+ soldering iron cleaner - There is a cleaner/tinner compound that when you put the hot iron tip into it, it cleans off the carbon buildup and tins the tip. Use it on a brand new hot tip before you do any soldering with it to condition the tip for use. A brass mesh cleaner is also good to have for cleaning excess solder from the tip, or you can always use a damp sponge.
+ digital multi-meter - one with more functions (ranges) is better, but at least one with voltmeter, ammeter, and ohmmeter. Auto-ranging is also nice if you can get it. Analog multi-meters are also very useful, but are more for finding the trend in a measurement rather than the exact value.
+ wire cutters and wire strippers - you can get all-in-one style, but I've found that most of the time the cutting portion is less than easy to use since it's between the handles. I prefer to have two tools. I highly recommend the self-adjusting automatic strippers shown in the image. A bit pricey but well worth it.
+ wire connector crimper - for attaching connectors to bare wires. Get a separate tool, or most strippers come with one built in.
+ wire nippers - like wire cutters, but they have a smaller jaw and one side of the blade is flat. This makes it easier to get into smaller spaces and cut closer to the board than regular wire cutters. They are also not as robust as cutters, so you can't cut larger gauge wire as easily.
+ precision screw driver set - both philips and flat-head drivers at the very least. Be careful with them as they are not at all strong (as levers go) and should not be used to pry things apart. Just saying. I also recommend a set of precision torx drivers. A small multi-driver set is really useful as well.
+ pliers - needle nose pliers are your friend. They are great for holding small parts so you can solder, adjust, place, etc. those parts. I also have a pair of vise-grips for when I need to grind something and don't want to get burned from the generated heat.
Step 2: Advanced Tools
Larger, more expensive, and/or not as necessary except for specific needs. Except for the rotary tool. Get that.
+ rotary tool - I would be lost without this tool. I use a Dremel 4000. Any brand will work of course, just get one with lots of accessory options so it's more useful in the long run. I use the cut-off wheel the most, both for cutting and grinding. Get a good set of accessories as well as this tool is so useful. Carbide bits will handle the finer metal work if you need it.
+ helping hands with magnifier - the magnifier isn't the most useful but the alligator clips are great for holding parts and wires in place so you can use your hands to solder.
+ small bench vise - for general holding and clamping.
+ organizer - you'll eventually end up with lots of parts, either stuff you bought or salvaged. You'll need to put it somewhere.
+ lighting - More is better. Much of what we do is small and needs to be close to the eye, so good lighting may help prevent eye strain. I use an Ottlite that I got from JoAnn's Fabrics. It gives a really good quality light spectrum so I can see what I need to clearly. (I originally bought for doing counted cross-stitch so I could distinguish floss colors properly :) I plan on adding some LED strip lighting similar to this in the future.
+ precision tweezers - for those really small parts that pliers may crush or are just too big to use with. Absolutely necessary if you want to be doing anything with Surface Mount Device (SMD) parts. (FYI - Some SMD parts, especially ICs, are listed as SOIC)
+ needle files - multi-packs are cheap and have several different profiles for various uses
+ hand drill and needle drill bits - if you do any PCB fabrication, you'll need to make some holes and full size drills can be cumbersome. I've used this very rarely, but it has been handy.
+ Jeweler's saw and blades - looks just like a coping saw but is meant for very fine work with metal. Good for precision cuts in small spaces. For larger cuts I use a hack saw because the fine teeth make for very clean cuts. An X acto razor saw would work well too.
+ hot-air tool - I use a torch with hot-air tip attachment. I like multi-use tools. Use it for heat-shrink tube. You can also get a hot-air gun. I would not recommend you use your wife's embossing gun. Just don't.
Step 3: More Advanced Tools
I use these all the time, but they can be pricey or require some more advanced knowledge and experience. Nothing a few hours browsing Youtube tutorials or forums can't fix though.
+ oscilloscope - any time you use a circuit that has an oscillating signal, you'll want this for trouble shooting. Any circuit that uses capacitors or inductors can suffer from anomalies related to unintended oscillations.
+ power supply - get one with both variable voltage and variable current
+ waveform signal generator - for testing new designs. Many circuits are useless if the signal frequency in is too high/low, so use this to test/troubleshoot as needed. I use the Digilent Analog Discovery, which is an o-scope, power supply, and waveform generator in one. It also has a spectrum analyzer and 16-bit digital signal analyzer/generator. It is the best bang for your buck that I've been able to find. The Electronics Explorer Board has the same functions and more, including more power supply options.
+ programming software - if you are using any kind of microcontroller, you will need a good programming environment. I use and recommend MPIDE since it is a multi-platform environment, capable of programming both Arduinos with Atmel chips and chipKits with PIC chips. It is styled after the open-source Arduino IDE, so it won't be hard to transition if you like. Here's a link to get you started with it.
+ circuit simulation software - there are lots of great programs, like NI MultiSim (<-recommended) and TINA. There are free programs as well, like LTSpice, though they won't have the same features of course. CircuitLab.com is a really good basic web based simulator that I've used many times.
Step 4: Resources
To get started in electronics, I highly recommend this course put together by one of my professors at WSU. Fair warning, there is a bit of theory behind the "why" and "how" of electronics.
A good site for project based tutorials is learn.digilentinc.com. There are many good projects on there, all related and ranging from analog to digital programming.
Some more sites I've found to be very useful -
I've been able to collect a number of great books over the last couple of years as well, most of which have been extremely good resources. Before you get anything else, find a copy of The Art of Electronics. There are three editions spanning many years, and all three are worth their weight in gold. I also recommend anything by Forrest M. Mims III, especially the 2 part Basic Electronics: Transistors and Integrated Circuits. The list goes on from there.
The Evil Genius series of books are lots of fun.
Of course my college text book is really useful, but about as much fun as a stick in the eye, so that's on you.
For components, there are a number of good places to start -
For microcontrollers, FPGAs, and the Analog Discovery, check out digilentinc.com.
Other good resources, and probably the best, are people you meet. It doesn't matter where you meet, like in class or a makerspace, or even a website that let's us all come together and share our ideas (I wonder where that might be!)
Electronics are fun! Don't get discouraged when it doesn't work. It will, just maybe not right now. Take your time, ask people, be safe, and above all HAVE FUN!!
Don't forget to check out the Digilent blog, where I contribute from time to time. And as always, please don't hesitate to ask questions in the comments. That way we all learn from each other. PMs are always welcome as well. Have fun building!