The first step you will take if you want to become a backup dancer is to become an excellent dancer through lessons and considerable practice. Once you have the necessary skills, you can audition for a talent agency to try and gain representation. Most backup dancers land jobs through auditions scheduled by these agencies. You may also be able to take part in contests to land positions as a backup dancer although these opportunities are less common.
In order to become a backup dancer you will need to gain several years experience in dancing. You should probably choose the exact type of work you want to do, since there is a wide range of dance types. Most backup dancers work in theater productions, although you may aim to work as a dancer for a major music artist in music videos or on tours. Both arenas are very difficult to break into, due to heavy competition. The type of dance you take will probably depend on the type of jobs you want to land.
Once you are accomplished in your particular type of dance, you should make every effort to be seen. You will likely begin by dancing in local productions and in local clubs. When you are confident in your abilities to perform in front of a crowd, the next step to become a backup dancer is to audition and land a contract with a talent agency.
Talent agencies employ experts in the various fields who have industry connections. Your agent will land auditions for you to give you a better chance of breaking into the field. Most big name productions won't see dancers who do not have an agent. Even if someone is willing to allow you to audition, you will usually be taken more seriously and given more consideration if you do have an agent. The talent agents work to find good talent, so those who are doing the hiring will assume that you have some level of talent if you are with a reputable agency.
Once you have an agent, you will up your chances of being able to become a backup dancer if you attend as many auditions as possible. Don't expect to land the job of your dreams the first time, but gain experience working in smaller productions first to add to your resume. Once you have proven yourself as a hardworking and reliable person, you will be much more likely to become a backup dancer in larger productions.