Flannel receiving blankets: Cut into 8" x 8" squares and zig-zag around the edges (or serged).
Inexpensive washcloths from the Dollar Store or elsewhere.
Any fabric you have laying around at home or even old t-shirts or cotton sheets.
Some great fabrics to use for wipes are: sherpa, velour, hemp fleece, and flannel.
There are many homemade solutions you can find on the web and make yourself. This is the one I like to use:
2 Tbsp baby oil (or olive oil)
2 Tbsp baby wash
2 cups water
Add water, then oil, then soap. Store in an airtight container (I use an old glass applesauce jar). Mix up fresh solution once a week.
I used to just mix this up in my wipes warmer and then dip my wipes in and wring out each time I use them, but lately (because I seem to go through it a lot quicker) I have been keeping it in a large glass applesauce jar (that is cleaned out of course) and shake it all up, pour some in the wipes warmer, and then store the rest of it in the closet in the baby's room. I occasionally will wash out the wipes warmer with baby wash if it starts to smell mildewy.
Another option would be to just use warm water to wet them or you can put the water/solution in a spray bottle and spray baby's bum with it, then wipe with a wipe. With the spray bottle you can take cloth wipes with you in the diaper bag and just throw in the spray bottle as well. It is just a matter of figuring out what you like and what works best for you.
If you have an old disposable wipes container, Kim with Dirty Diaper Laundry shows an awesome way to fold cloth wipes together so that they pop up out of the container with each pull of a wipe, just like disposables do. Pretty nifty and quite convenient. You can put your wipes in the container and then just pour the solution over it and store in there if you go through wipes rather quickly. You just don't want it to start smelling like mildew or grow bacteria if it takes you a while to go through very many wipes. Try putting in half the amount of wipes.
Remember, you can still use disposable wipes while cloth diapering if you choose. I usually use these away from home and you can just throw them right in with your diapers and wash, then remove from the washer and put them in the garbage before transferring them to the dryer (causes lots of lint and there is no sense in drying something you're just gonna throw away).
Cloth wipes do a great job of cleaning up, especially because they are more like a washcloth than a paper towel.
Now go get you some cloth wipes and give 'em a go!