How soon is too soon to move on to someone else after a break up ?

If you want to be fair to any new partner then you should get over your relationship first, as @Jessmari said already. Nobody wants to be the rebound.

If it's just casual and/or sex then as soon as you like. Just bear in mind that what you do after a breakup might affect any chances of ever getting back together with that person. Not that you should focus on getting back together with them, it's just worth noting.