Brookelynn--
Great question. I am on my third national tour and the third company in three years. I sent my resume what felt like a million times before I got hired.
It isn't always easy to get on a tour. I found the best thing to do is to send your resume. There are quite a few companies that tour I'd start with, NetWorks Presentations, Phoenix Entertainment, Trokia, Big League and Work Light Productions. Most of those company do non equity work, but they occasionally do equity work. Another thing to try is to shadow a show when it comes through town. Or if a tour happens to be doing their technical rehearsals in your city being a PA for them is also a great way to make connections. A lot of this hiring is based on who you know and being in the right place at the right time.
Best of luck!