Hand-dyeing is perhaps a bit messier but just as easy as machine dye. I use a washing up tub or else the old baby bath if I'm doing a few things at a time. Usually all you have to do is soak the nappies, mix up the dye and soda ash (it may come with a kit if you buy one) and add the nappies! and stir for 10-20mins. If you dont stir, it may be uneven but i dont usually mind that.
LWI, as Hanna said, is Low water immersion dyeing and she's well renowned for that you just place the damp nappy into an ice cream tub (or such) with an inch or two of water in the bottom - just enough to come about half way to 2-thirds up the nappy. then pour dye over, several different colours in different places. Leave it to soak for a little while then rinse, and you've got lovely dyed nappies!
Ive never tried tie-dyeing non flat nappies, it might be hard to do right as they are so thick and washing machine tend to be very effiecient at getting the dye in all the nooks and crannies. While you're at it, why not get some white t-shirts and vests etc, and dye some to match the nappies?