Gain the rights to do the play. While this does not have to be done immediately, if you do not get the rights to produce the play, everything else you have done will not matter. Many plays provide ways to contact the author or the author's agent within the first few pages. If it's a new play, the information will often be on the title page.
Assemble a production team. Depending upon how high or low budget your production is, this will include a various number of artists. A director, set designer, costume designer, lighting designer and stage managers are all great additions to a production. One person can do many of these jobs, but often efficiency is sacrificed. All of these positions are somewhat negotiable; however, the abilities each provides will have to come from somewhere. The actors might provide the costumes, and the director might also be the set designer, for example.
Hold auditions. Find an audition space, and announce the auditions for the play. Then cast your actors for the production.
Meet with your production team to get everyone on the same page. For example, the costume designer and the lighting designer should know what colors each of them is planning on using. The costume designer will want his costumes to either blend in or pop against the colors of the set designer's set.
Read through the play with all of the actors. This will give everyone a feel of what the play sounds like before getting on their feet. Keep everyone seated. This way the actors can focus on their voices and some of the emotional connection from a psychological level.
Block and rehearse the play. Get the actors on their feet, and work through the scenes one at a time. You can either rely on the actors' instincts and select what's working, or you can have a more hands-on approach and set up their preliminary blocking before they begin to work. Setting up the blocking ahead of time may give the actors an idea of where you're going, but you should be flexible in changing the preliminary blocking. As the actors get more comfortable they should begin "run-throughs" of the play.
Add technical elements. Add aspects such as costumes and lights. If you have other set elements to add, this is the time. This should ideally be done the week before opening.
Open the play.