Okay, well, the process of play production can look a bunch of ways depending on what level your play is, whether it is a professional or amateur production. And, if it is professional, whether it is a for-profit or not-for-profit venture. Also, different artists and different theater companies have different styles. For example, I belong to a company where we create plays as an ensemble by engaging with our community. So, we will 1) do a series of community events and interviews 2) decide the main production team (director, lead playwright, assistant etc.) 3) workshop our findings into a script 4) so a series of public and private script readings for feedback and revisions 5) secure the venue and begin the long and hard process of creating a marketing plan for the play 6) hire the rest of the production team (stage manager, production assistants, designers 7) cast the play 8)rehearse the play while also carrying out the marketing plan (as well as keeping up with the financial administration 9) do the play
It is more traditional to start the process with a play that has already been written, either a new play or a classic play that people want to revive. After that, many of the above steps are pretty much the same.
Good luck with your play!