It certainly depends on one's own moral structure and the validity of the previous relationship. If the previous relationship was not marriage or a long term commitment and if you no longer have feelings for your previous relationship you can begin dating as soon as you like. But morally speaking, if you think that your previous boyfriend/girlfriend are not ready to see you moving on, then perhaps subtlety would be the right way to handle a new flame. Try to avoid their normal hang outs, restaurants or bars. Allow them time to move on, without flaunting your dates. Giving them space to get through the break up, is the right thing to do.
If the relationship was a lengthy committed relationship such as marriage or a similar union, then considering the affects of it's end would be wise for you both. After the end off a long term relationship, you need time to "find yourself" again. You are different now, than when that relationship began. But now your need to learn to be yourself, by yourself before jumping into a relationship with someone else. Too often we are so comfortable with being in a close relationship, we begin another too soon. This is not fair to your new "love" as they are not the same as your previous relationship, but some of your expectations from them may be.
Allowing enough time for your to heal, and know what you really want, in the next stage of your life, will help to build a stronger relationship later.

It depends on if you were the one ready to move on. Then you were ready and so you are probably ready to casually date.
To jump into another relationship I think would take a little longer. Everyone needs a little time to analyze what the good and bad in a relationship that failed was, and how not to repeat the bad aspects.

It would depend on the length of the prior relationship, and what kind of relationship it was. Are there children involved?
But I don't believe in a set time period. One person may be ready in a month, someone else may not be for a year.