Budget for submissions. No matter which of the following methods you choose, each one has a financial cost tied to it.
Build a website. Many companies are accepting online submissions or interact with potential talent online. Having a website that showcases your background and music lets interested parties know that you're serious about your craft. It's important to update it regularly with new musical compositions as well as relevant articles and videos.
Send a demo to music publishers. Publishers specifically are interested in maximizing the potential of a song because they have a personal stake in it since they contract to take a huge percentage ownership of a song. They leverage their contacts and talent to place music a in variety of different arenas of which film is just one. Many have their own websites or can be found in specialized listings like the Songwriter's Market, a yearly publication listing of music-related companies and organizations looking for original music.
Join TAXI. TAXI is an artist and repertoire (A&R) firm that places music for several different companies including record companies, music publishers, film and movie creators. There is a yearly fee of a $299. TAXI releases a list of current jobs available twice a month that members can submit online. Each song submitted has a minimum $5 submission fee which comes with a full critique. Every song submitted does not get passed on to the listing company, as TAXI screens incoming songs for quality and appropriateness. This can get pricey so it's important to submit relevant music of high quality to the relevant listing.
Join Sonicbids, which is primarily a place for bands to acquire gigs. However, it also lists licensing placements for music for film and television regularly. Members can build their own online electronic press kits, promote their music, and browse the listings. Submission fees are anywhere from $5 to $12, or tokens can be purchased that allows for a set amount of submissions.