Contact the theatre and ask to speak to someone in charge of costumes. Smaller theater companies will likely not have a separate person running their costume department; in such cases you will be talking to a director or president of the theatre organization. Inquire if they need or want the costume that you are offering. Describe the costume accurately and concisely. Theater companies may refuse the costume because they already have too many of a particular type of costume. Some theaters will offer payment for costumes rendered but usually only if they are currently doing a show where they require that particular costume. Otherwise they likely do not have a budget to buy a costume.
Set up an appointment for them to see the costume. The company will need to view the costume to make sure that it is appropriate for their productions. The quality and appearance of the costume will be an issue to them, so just because they say they are interested, don't assume that they will be accepting the costume in the end.
Repair all rips, replace lost buttons and make sure seams are folded and sewed properly. If you are able to make the costume stronger, by reinforcing stitching, then do so. Costumes go through a lot of wear and tear when they are used onstage and the company will be more likely to accept a costume that is sturdy. Use needle and thread to hand stitch any repairs. Hand stitching is more secure and exact than machine stitching and for theater, you do not see the little details onstage, so hand stitching is usually the best choice when repairing a costume. Also, hand stitching is easier to remove if the theater company want to adjust the outfit to suit a particular play or actor.
Clean your costume by following the cleaning instructions as outlined on the outfit's tag. If there is no tag, find out what type of material from which it is made and follow the typical cleaning instructions for that fabric. A seamstress may be able to help you identify the type of fabric and advise you on cleaning instructions. Acceptance of the article of clothing by the theatre will depend on the cleanliness of the outfit.
Arrive on time to the appointment as not to waste the theater practitioner's time. Show the theater person the outfit and answer any questions they may have about it. If they accept the outfit, then fill out paperwork for the transaction if applicable. If they do not accept the outfit, then contact another theatre company to inquire if they are interested.