Over the past several years, there have been several threads about home-brew LP cleaning solutions that A-gon members have found to be effective. You can find these threads by looking in the A-gon archive.
At the risk of being repetitive, I'll offer the formula I use:
1. Take 1 gallon of distilled water, and remove 1 pint (keep the pint for another use, or drink it...).
2. Add 1 pint of 99% pure isopropyl alcohol (available in many drug stores) to the gallon container of distilled water. Note: DO NOT use rubbing alcohol.
3. Add 1/2 TSP (or more, if needed) of a surfactant to the distilled water/alcohol mixture. Surfactants can be acquired from chemical supply houses or places that sell dark room photo developing supplies. In a pinch, you can also use a good, non-scented brand of household dishwashing detergent (I suggest one of the clear ones).
If you look at the threads in the archive, you will see that some people say to avoid using alcohol in LP cleaning solutions, due to concerns about removing the stabilizers in the vinyl. I can only say that I have used my cleaning solution with my Nitty Gritty machine for over 25 years, and have cleaned more than 2500 LP's without any damage, so I am quite comfortable recommending it to others. It's also cheap to make...
After cleaning an LP, I strongly recommend the use of LAST record preservative. Good cleaning followed by treatment with LAST has kept my LP's (some of which I've had for more than 30 years) in fine condition, even after repeated playings.