I, uh, take mine apart.
The toughest thing about the Ruger 10/22 mags is getting the rotary follower reassembled with the right amount of spring tension. Too much or too little will cause feeding and functioning problems.
However, if you're not as adventurous as I am about disregarding the manual instructions, I'd either use a aerosol gun cleaner spray, making sure to test it before you use it for compatability with the plastic the magazine is made out of (the Birchwood-Casey GunScrubber softened the stock on my DISC with just an accidental overspray). The other option would be to flush it out with hot soapy water. That would take the bulk of the powder residue, lead and copper flakes and dirt out of the magazine. Obviously make sure the magazine is dried and lubricated with CLP or something similar after you're done. Don't overdo the lube, you want to prevent rust, but not provide a oily mess for more crap to stick to.
Mike