Two primary ways to acquire a ship of your own:
1. Save up money (faction salary is a good start) and buy a ship from another player. This can be done via the GM (www.swc-gm.com) or the Commerce section of the RP Centre or #swc-traders on IRC. The ship will not appear at your position, though. Someone would either need to transport it or transport you to it. Ships cost upwards of 100K, often into the millions of credits.
2. Acquire enough CPs to buy a ship of your own through the CP exchange (click your CP amount and follow the Support the Combine link to click the CP banners, which you can do every day, or you can donate to SWC). If you aren't willing to donate, obviously this isn't a very good solution. ^_^
However, if you join a faction they should assign you a ship that you can use. You won't own it, but they should transport you to it.