I've just recently gotten one of those fancy record cleaning machines, so I've been researching this question a lot. There are a bunch of moderately expensive fluids out there, but the Library of Congress recommends a mixture of about two parts distilled water, one part isopropyl alcohol (get the techincal or lab-grade stuff, not the drugstore kind that's only 70% alcohol with too many impurities) and a couple of drops of some kind of surfactant to make the mixture "wetter." The surfactant could be good-quality dishwashing detergent (like Dawn or Palmolive), or Triton X-114 or Monolan 2000 from a lab supplies place.

Don't use any alcohol on 78s; it will eat the shellac and ruin the records.

Dribble some of the mixture onto the record and work it into the grooves with a brush. You can buy a special brush from VPI or Mobile fidelity, or use a relatively soft nylon paintbrush.

The advantage of the cleaning machines is that they vacuum up the fluid after you spread it around with a brush, and they take the crud that you have loosened from the grooves with it. If you don't have a machine, use a dry, soft lint-free cloth to remove the fluid.

As you might expect, there are several web site that offer advice about cleaning records, with and without a machine. Google "record cleaning" to find more than you would ever need to know.