This instructable, and its videos, show two of the simplest modifications that can be done: pitch bending and body contacts. I've deliberately not shown some of the more complicated methods, like triggering samples using a timer circuit, that you can learn once you've got the basics down.
Most steps have videos that carefully go through the processes described in the text. I see them as vital tools to help you see how this is down within a real circuit.
Difficulty: beginner to immediate
Skills needed: basic electronics (know about resistors, power, ground, switches), soldering (although this is an easy-enough project to get or build soldering skills)
Step 1: Materials and tools
Onto the list of things you need!
Toy: Obviously you need a toy to modify--one that you don't mind opening up and (potentially) making inoperable if something bad happens. I recommend the usual places: thrift stores, surplus stores, etc. But...please, please, please, PLEASE don't go to a major retailer and purchase something new to modify. There are enough toys out there on the market being discarded---we don't need to give multinational corporations higher profits by buying something new when we can reuse and modify something that already exists. So go to your thrift store and scrounge around; you might not find something immediately, but be patient for the right toy to come along.
The best toys are the ones that aren't complicated: only a few sounds, a few buttons, etc. Anything that has complicated behavior is going to have complicated circuitry that is both going to be more difficult to modify and more likely to simply screw things up without making useful sounds. A good beginning toy to bend would be a stuffed animal that makes a few sounds...open up the toy and you'll find inside a plastic case that has an extremely basic chip. In my case, I chose a toy designed for toddlers that has only a few buttons and sounds--meaning the circuit inside will be relatively straightforward.
And it should go without saying (I hope)...but don't bend anything that requires a connection to the wall or mains! ONLY BEND TOYS THAT USE 9V BATTERIES OR LESS!!! I'm certainly not responsible if you hurt yourself doing this...you shouldn't, if you bend battery powered toys. But no warranties, etc. legal mumbo jumbo.
Electronics: For this bend you'll need a random assortment of parts: on/off switches, some resistors, a potentiometer, and wire. To attach things you'll of course need a soldering iron and solder. And to test things out, some alligator clips are really useful.
Other tools: A drill or dremel to cut holes in the casing, and a screwdriver to take the case apart.
The video for this step is me playing around with the toy before any modifications are made.