Advertise online and in print publications. There are sites such as Craigslist where individuals can advertise for screenwriters free of charge. Seek out film publications, and the methods and costs in which you can place an ad for your search. Some of them can be expensive, but may be well worth the cost if you locate a quality individual who is interested in working with you. Many film and screenwriting associations also have websites where free ads can be placed.
Attend screenwriters' meet-ups and film gatherings. If you live near a large city, there are usually many writers' groups that meet regularly, and they are a virtual goldmine in locating professional and aspiring writers. Call the contact person or president of the club ahead of time and let her know what you are looking for. She may have some suggestions for you to follow up on even before you arrive at the meeting. Ask for a chance to speak about your search and requirements; there almost surely will be a person looking for a chance to prove himself in the film industry.
Contact film agents, actors, directors, producers and anyone else who may be involved in film. They would know of reputable writers from their past film work and current associations that may be able to help you tell your story in a personal and professional manner. Their input is especially helpful, as they will have had firsthand experience in the filming of specific screenplays and would be knowledgeable in the quality of an individual's scriptwriting skills.
Make an appointment with the head of your local or state film commission. The purpose of this state or city office is to encourage and assist filmmakers in writing and producing movies within their area to provide jobs and area growth. They work closely with everyone in the community who is involved with the movie business. They will be only to happy to assist you in your project, especially if there are plans to film your movie locally after it is written.
Visit the writing department of local colleges and universities. Meet with teachers and professors to find the best screenwriters from the student body and offer them an internship or part-time job writing your story into a screenplay. This is a great alternative if you are on a limited budget, and you may be pleasantly surprised at how talented some students are. They will work very hard for a course credit, minimal pay and a DVD copy of the finished movie.