When it comes to getting back together with an ex, is to first establish what caused the breakup. Understand that you cannot go and change what may have happened, but accept what happened and see it as something that you can learn from.
The first step is to figure out what caused the breakup to occur, this could be anything from on event that may have happened, many events that added up, gradual loss of interest, etc. The point here is to be able to pinpoint the reason that caused the breakup.
A great way to work in the beginning steps of getting your ex back, is when you speak or interact with them, that you don't express yourself as being a needy person. Do not plead to them or tell them that you cannot be without them; this will most likely drive them further from you. What is important at this time is to be strong, allow time for your ex to realize that you are confident and self-sufficient. Be happy for yourself, and be sure to show that you are!
When you can easily assume that your ex has realized that you are happy and content with things, and that you are a strong person regardless of what may have happened, you should look into contacting your ex. This could be by phone, or meeting somewhere for coffee, just something similar to a friendly get together. Be absolutely certain that you know what to say and when to say it, because when it comes to getting your ex back this is not the time for error, so get it the first time. Simply ease into the topic of what may have led the relationship to where it ended up, simply talk about what happened in a dignified and mature manner. Don't come off as a needy person or that you are completely in need of them. Just allow them to be able to figure out that your friendship is something to appreciate, and over time it will become stronger.
Over time their feelings show grow, and when this is obvious, make plans then to make your move in getting back with them. Ask them to go have dinner with you or to see a movie, or to just have a fun time with just the two of you. Then you can make the judgment of asking to have them back with you.
When it comes to getting your ex back, understand that it takes time, and do not rush things, slowly ease into these things, and develop the connections you and your ex once had that made the two of you want to be together in the first place.