In mathematics, subtracting a negative number is the same as adding a positive number. It is the same in life and love. Subtracting a negative situation, or specifically, a negative person is a positive. This is the first thing you must acknowledge when going through the ordeal of a breakup, the mourning/solitary period, and the deep breath required to try your hand again. If the previous situation was as good for you as you thought it to be, it would still exist. That isn't to say that there is no hope for rekindling of lost romance, as there are many stories of people who break up a hundred times and end up married for the rest of their lives. This blog is for those who have decided to put something that most certainly cannot work behind them. If your sense of self-worth was derived from how that person felt about you, the relationship was unhealthy; if it wasn't, then you should have no qualms about saying "his/her loss". Because it was. If that person felt the same way about you, you'd still be together.
The first step isn't easy, as it requires the sort of introspection that is commonly ignored in favor of good old-fashioned denial. It requires accepting responsibility for the part of the breakup that was your fault and your fault alone, NOT inheriting your partner's shortcomings and falling into that well of self-loathing, but acknowledging what you could have done better. This isn't psychology (not really), it's a necessary, grown-up thing that must be done in order to first forgive yourself, and then be sure the cycle doesn't repeat. Nothing kills a potential romance like a trunk full of baggage. You begin to paint the new interest in the same shade as the old one, and it becomes impossible to see the new person clearly.
The second step is ensuring that the alone period, the "me time", was fruitful. Essentially, that you've spent enough time time by yourself to fully understand what you want in a mate. Otherwise it's just trying on shoes. Self-knowledge will also prevent you from trying to live up to expectations that aren't within your repertoire. If you're not down with threesomes, it's best not to allow the possibility to grow in your partner's mind. If you hate reality TV, playing along with someone who is obsessed with them will grow stale after some time. Not that small things shouldn't or can't be overlooked in favor of the complete person, but altering another's ideals or their way of being will only cause them to resent you, unless it is 100% for the better ("better" being a matter of perspective).
The final step is, of course, the hardest. Putting yourself out there. Being vulnerable again. Learning to trust yourself not to fall for the same thing(s) you did before. But you can't remain a closed book and expect others to feel invited. Sending mixed signals can put off an air of mystery to those with a good bit of patience, but it can also be confusing to those who expect you to be upfront about your situation. The reality is that the aforementioned-letting go of old business and getting to know yourself-is what will give you the will and the strength to keep trying, for better or for worse.