Here's another older project that originally appeared on my old "synthgeek pages" blog. Like the TrigPulser Mini posted earlier, it's relatively simple, runs on a 9V battery, and may make a suitable beginner's project.
This one uses two IC's: the venerable 555 timer, and the LM567 tone decoder, which is used here for its amplitude modulation capability and built-in oscillator. The two chips are set up in a sort of feedback loop, where the 555 is used an an oscillator to feed the 567's AM input, and the output of the 567 is fed to the CV input of the 555. Switched jacks are used to provide inputs for the AM input on the 567 and the CV input of the 555, such that plugging something in cuts off the internal connections. The schematic includes a similar setup for the output of the 555, so you can also use that as a seperate sound source if you like.
Here's an older "guided tour" video:
Note that although it can be used with external signals, it isn't tuned to be compatible with any modular standards out there or anything. It should work, but won't accurately track pitch or anything like that. In my own setup, it tends to get used mostly by itself, or with my Lunetta stuff, which is similarly lo-fi. Here's another video of the Messmaker making noise, this one's in a black VHS case:
Photo with controls & stuff labeled:
Here's a shot of the board from the first one I built:
...and here's the schematic, including a parts list. Note that J2 is the "main" output jack, you can leave out the rest (J1, J3, J4) if you don't care about doing the "semi-modular" style.
If you have any questions, feel free to ask in the comments, and I will try to answer.