To purchase ships or vehicles, you will need credits (typically acquired via faction salary). After that you can start trading. The most common place to purchase assets is the GM: http://www.swc-gm.com
At this time you can only purchase assets from other players, and the GM is a sort of eBay service for SWC, so you will need to carry out the transaction through the SWC interface - the GM won't do it automatically for you.
You will likely not have enough credits right away to buy much, but your faction should assign you a ship to use in the meantime, and should also provide you transport to that ship.