You can get random prime parts from void fissures and sell them in trade chat as 'prime junk' to make a small amount of platinum, and use that to buy the slots. You can buy platinum with real money, of course. We all face the same issue of having to spend platinum on weapon and warframe slots. The only way to free up slots is to sell your weapons for credits. So you can't trade fully-levelled weapons. Once you take it into a mission, it becomes untradeable. Most weapons are untradeable when fully built and those that are tradeable, become untradeable once they earn any affinity (experience). You can't trade weapons, as a basic rule. You start the game with 50 (?) plat I'd suggest spending it on a warframe slot (20) and 2 pairs of weapon slots (24). The only way to get more is to buy them with platinum.
So yeah, there are a limited number of inventory slots you get.
