The first step is to address the problem. For many the problem can be evident and obvious, such as a cheating partner, or financial troubles. Other times you must look deeper and go beyond the obvious and put your relationship under a microscope. Many problems can be indirectly caused by small things that you wont see.
Once the problem is identified you must then establish your feelings on the situation. Rationality is what you must strive for here. Problems can and usually will lead to the rise of strong emotions, your do not want to suppress these, but rather have them work in tandem with rationality. By keeping a level head you put yourself in control of your individual situation.
Communication is now what you need to save your relationship. It will act as the main supports that hold your relationship up. As you start talking with you partner keep in mind that they might not see a problem and may become defensive at the notion that your relationship is jeopardy. Be careful during the initial communication process as to not alienate your partner so that they remain open to further discussions which will be the processes which begin to rebuild your relationship.
Now that you've begun the process of saving your relationship by starting lines of communication with your partner, you must keep one thing in mind, you must allow your partner to say what they need to say. Many people may speak harshly and untruthfully, saying things that they do not mean, or that they mean only to hurt someone who they feel has hurt them. While you must keep this understanding towards what they say, do not be nieve to signs of true maliciousness.
Now that your communication is evolving you must begin to attempt to see the situation through the eyes of your partner. You must decide whether or not they see a relationship worth saving. Many times a partner can feel it is easier to end it rather then save it, if you believe this is true you must make them see that this relationship is worth saving by reminding them of what you had, or by starting over with them and building a new relationship.
You can decide which course of action is best by looking at your past. If your relationship has withstood hardships before it is very strong. By reminding your partner of these hardships you can make them see that your relationship has something special. If you are concerned that you don't have this inherent strength you must rebuild by going back to when you first met and bringing up those old emotions to rekindle the fire.
Through all the trials and tribulations of attempting to save a relationship you must always remember to stay level-headed and always communicate clearly. If you can manage that while practicing understanding you can gather the pieces and put your relationship back together.