Ask friends or family members to read over and check your work. Before you submit your work to agencies or production companies you want to make sure that it is the best it can be, so ask friends and family to read it over and use any criticism in a positive way to improve your work.
Enter contests for screenwriters. They are constantly running and can be found by a simple Internet search. Contests are a great way to improve your writing and if you do well you could gain the positive exposure you need to push your writing career in the right direction.
Write a spec script. An important part of becoming a successful television or movie writer is being able to write a good spec script. This is a script for a show or movie that already exists and should demonstrate your ability to write professionally. For example, if you are interested in writing sitcoms then you would focus on writing a series of spec scripts for different sitcoms that are already in production.
Write to agencies. If you have no previous experience writing for television or movies then you should apply first to relatively small agencies. Send a query letter and an example of your work and try to sell your talent to the best of your ability. It can be difficult and frustrating to try to get an agent; however, persistence is the key and sooner or later you will find someone who wishes to represent you.
Write to production companies. Send a minimum of two spec scripts to production companies. Be careful not to send scripts of their own programmes as they are likely to judge these with unfair expectations and there could also be legal issues if you claim they used ideas from one of your spec scripts. Instead send scripts of programmes of the same genre.
Don't let rejection get you down, don't give up hope. As a writer, you are constantly gaining experience. Continue to submit work to agencies or production companies and eventually your persistence will be rewarded.