Electrophoresis does require some equipment to perform -- an inner tray which holds the gel, an outer tray which holds a "running buffer" solution (which keeps things cool and keeps pH stable), electrodes, and a power supply (50V-150V is pretty common). You can buy a gel box from a commercial supplier, though they're not cheap, and a fancy power supply will set you back even more; Bio-Rad has some nice ones, but they run to the thousands of dollars.
Happily, there are solutions for the biohacker on a budget. The University of Utah's genetics department has full specs for how to build your own gel box for about $25 in parts (not counting the power supply, which will run you about $50). The main components are clear acrylic and acrylic cement, which I purchased and had cut to size at TAP Plastics -- they also do mail order. My partner-in-science Tito Jankowski built one too, and did some test runs with food colouring which enabled him to separate the individual dyes which make up different colours. (The molecules in food colouring are pretty small, which is why the bands in Tito's video are a little smeary. He used agarose -- an edible, seaweed-derived polymer which you can find on the shelf in any Asian grocery store, also sold as "vegan gelatin" -- as his gel, and agarose is better suited to larger molecules like DNA. But it's definitely a proof of concept!)
Still, electrophoresis using large rectangular gels has some drawbacks. It's a bit messy, and in order to recover the particular band of DNA you want, you have to slice it out of the gel with a razor blade or something similar. Cleaning up the equipment is also a bit of a pain. If you're using acrylamide or polyacrylamide (common for protein electrophoresis), you need to find a safe way to get the used gel out of the gel carrier and dispose of it properly. Also, while DNA electrophoresis is run horizontally, protein electrophoresis is done vertically, so that means two different pieces of equipment.
This was a recent topic of discussion on the DIYbio mailing list. Ben Lipkowitz wondered whether it would be possible to use a narrow, rigid tube to contain the gel, rather than a big carrier. This would allow for the use of less buffer and lower voltage, since a physically smaller amount of gel is a smaller resistor.
Well, what's a narrow rigid tube that's easy for anyone to acquire? A clear drinking straw! Paper clips make for appropriately sized electrodes, and since a drinking straw is rigid, it can be used in either the horizontal or the vertical orientation. For extra bonus points, when you're ready to cut a band out of the gel, no need for mucking around with razor blades -- just take a (sterile) pair of scissors, snip snip, and you're done! Plus, disposal is extra simple, even with polyacrylamide -- just dispose of the entire straw, gel and all, properly.
Tito Jankowski tried this out, using a single 9V battery as a power supply, and after some debugging, it worked beautifully. (He also used alligator clips as electrodes, and they worked just fine.) We're calling these "keiki gels" because they're so small and cute -- and so simple, even a little kid can do them.
This is crowdsourced science at its very finest. Behold the power of collaboration!
ETA: Tito wrote a protocol, doo dah, doo dah