I have no experience with the AIVS fluid mentioned by several others above, but for years I have made my own "home brew" cleaning fluid for use with my Nitty Gritty cleaning machine. If you're on a budget, you might make up a batch of my formula and try it -- and then if you are not satisfied, by all means check out AIVS.
Here's how I've made the solution to clean my LP's for the past 25 years:
1. Get a gallon of distilled water, and empty one pint from the bottle (to make room to add the next fluid).
2. Add one pint of 99% pure isopropyl alcohol to the water. (Do NOT use rubbing / denatured alcohol -- use only 99% pure isopropyl, which you can buy in many drug stores.)
3. Place 10-12 drops of a surfactant to the solution (you can buy surfactant at a chemical supply house, or simply use a good quality liquid dish detergent).
There will inevitably be some of our forum readers who will disagree with the use of alcohol-based solutions for cleaning LP's, but based on my own empirical experience I have never had any damage done to my records, and I am still enjoying them after many years.
The last step I recommend is to treat your LP's with LAST record preservative after you clean them.