Variables taken into consideration
1) Type of Pot: Cacti in clay pots require more watering than do those in plastic.
2) Pot Size Generally the larger the pot the more infrequently it will require watering, and conversely the smaller the pot the more frequently it will require watering.
3) Species also dictates water requirements. Some are very "thirsty", and others will not tolerate over watering.
4) Light . The amount of light a cactus receives also dictates its water requirements. Plants in darker areas require less water.
5) Season. Do not over water in the winter or in a dormant period as it can lead to root rot and collapse of the plant. Watering in winter also leads to atypical growth patterns, due to reduced light levels. You can mist or spray your plants in the winter to avoid shriveling. As you get to know your plants and their water requirements you may develop a watering schedule, however it is always safer to err on the side of caution.
6) If in doubt don't water. Cacti can survive many months with no water, especially in winter
For the beginner I would recommend a moisture meter as it is difficult to gauge moisture content of soil by touch alone.
I prefer to water most of my cacti from the top, that is to pour water right on top of them. I do not however pour huge amounts of water onto the cephalium of melocactus and discocactus as it tends to wash the cephalium away. I also avoid watering from above the fuzzy crown of echinocactus, and any "hairy" cacti such as oreocereus for the same reason. When watering, give enough so that the water runs freely from the drainage holes.
The most common indicator that you are over watering unfortunately is a sudden collapse of the plant commonly known as "black rot". Initially the roots rot from the bottom up, so the damage does not seem apparent until cooler weather arrives. If you see black, mushy areas of tissue usually around the base of the plant it is time for immediate action to save the plant as the infection can spread quite rapidly. All infected tissue must be removed using a sterile, sharp cutting tool. Make sure you cut into healthy tissue and ensure all diseased tissue is removed. The last cut into healthy tissue must be with a sterile blade. Apply rooting hormone to the exposed tissue, and allow to callous over. (treat as per cuttings.)