For used records that I purchase, I use running warm water, a few drops of dish soap, and a nylon bristle paint brush. I hold the record at an angle under the water when wetting / rinsing it, as to not purposefully get the label wet (if I do get it wet, I quickly dry it off). I use the brush to work the water / soap into the groove, brushing in a circular motion in the direction of the grooves. Once I'm finished washing / rinsing, I used compressed air to blow out / off any residual water. Works well.
For incidental record cleaning I use a 75% / 25% mixture of IPA and distilled water in a spray bottle. I keep 2 premium car polishing cloths in a zip lock bag, I use these cloths to lay the record down onto and to wipe the record down.
I have also tried disposable eye-glass cleaning wipes. They are sold by the box, and contain individually sealed / moistened wipes (contents differ by manufacturer, but most of them are a Isopropyl Alcohol / water mixture). I typically wipe a single record and dispose of it.
So many opinions and individual techniques out there, these are the ones that I feel have worked best for me over time, with no noticeable negative effects to my vinyl.