Let's take 3 scenarios to discuss (feel free to add any other situations and their proposed solutions):
1) The breakup was mutual, and not on ugly terms but you realized later on that you want them back
2) The breakup was 1-sided, they broke up with you for a particular reason (loss of feelings, you're not doing enough for the relationship, etc)
3) The breakup was 1-sided, you initiated the breakup but decided to change your mind subsequently; to which they turned you down the initial time you tried to get back together.
Under these circumstances, would it be best to leave them alone for now to give both parties space, chase them and hopefully convince them to be part of your life again, etc?