Step 1: Stepping Down the Wall Voltage
These transformers that I bought did not really have any information provided about them, and I would guess that any scavenged parts would likewise be as much a mystery. The primary side was easily identifiable by the heavier gauge of wire. A scavenged plug was soldered onto the primary, and the connector was lopped off of the secondary, as I wouldn't use it anyways.
An important thing to thing about, if you get any say in the transformer that you are going to use, is how much current that you are going to draw from it. Size seems to be an indication of how much you can draw, but here, if it isn't listed somewhere, I usually go ahead with it and check to make sure it isn't heating up too badly at the end of it all.
Any Time You Are Plugging Anything Into the Wall, Be Extra Careful About Where You Put Your Hands, and What Conducts Electricity!!!
Step 2: Rectifying the Stepped Down Voltage
My preferred method of doing this is the use of a bridge rectifier. There are a couple ways to do this however, if you have rectifier diodes hanging around from something else that you have taken apart, you can build your own easily. Or, you can get one of the prepackaged ones that are available from Fairchild or other component companies.
Pretty much the only thing to worry about is to make sure that whatever you are using will be operating within its range. Check any available data sheets to make sure that you aren't going to try and pull too much current through the rectifier. If datasheets are unavailable, i.e. you used scavenged diodes to build your own rectifier, I usually just go ahead and build it anyways, and see how much everything heats up.
Step 3: Filtering
This is a really easy step, especially since electrolytic capacitors are common, and you probably have something broken lying around that you can pull one out of. Here, a larger value is better, but you don't really need to go overboard. I just put in a large value and then later replaced it with smaller and smaller values until the ripple got bad enough for me to worry about it.
As with all things, make sure that you are using a component that will work within its safety limit. Here, you have to make sure that the capacitors rated voltage isn't exceeded. It would be a good idea to measure this just to be sure.
Also: Make sure to put the capacitor in the right way. The side with the stripe on it is the side that you must put to the most negative voltage. I've only ever seen it once, but when an electrolytic capacitor is put in backwards, it can explode.
Step 4: Regulation
Again, you could do this step in a couple of different ways. First you could whip up a zener regulator, if you happen to have zener diode around that fits the output voltage you wanted.
Personally, I prefer another way. More of a 'plug and chug' approach, this method just uses a prepackaged voltage regulator readily available from any number of different companies. Pretty much all you have to do is make sure that it will handle the current you are going to pull from it, and that you are supplying it with a voltage inside of its input range. One of the ones I built needed to have the voltage dropped down a bit further so I figured out the size of the resistor needed to put the input voltage inside the proper range. If you need to do this, just keep in mind the power dissipation.
Also, some regulators need a small capacitor in parallel with the output in order to stabilize it. The datasheet will mention if it requires one or not.
Step 5: Other Safety Considerations and Finishing Up
Just watch, what you hook up to it, so that you don't fry any of the components, and be really careful with that transformer, as it is plugged into the wall.