Warframe's really bad at explaining itself, unfortunately. The codex (near where you start on your ship) has a tutorial section worth reading, which will explain the basic controls and concepts.
For everything else, use the wiki. I've sunk almost 200 hours into Warframe and I'm still looking things up daily.
There's also the
PC or
PS4 OTs, which have a nice community and are a big help for broader questions or chat.
In general, you'll want to Always Be Levelling™ so you can improve your Mastery Rating, which will give you access to more stuff and improve your capacity for some things. Unlocking
Junctions is a secondary goal early on. Alternately, you'll want to decide on specific loadouts and perfect them so you can tackle late/end-game content. Note that mods are more important than an item's level, and the drop rates/drop conditions on some of them are bananas, so you'll see wildly different levels of power from similar warframe set-ups.
Oh, and if you've ever considered buying platinum (the paid currency) note that there are occasional coupons you get via daily log-in bonuses that apply to them, so try holding off until they appear. I've seen -20%, -50%, and -75% off. Platinum adds a lot of cosmetic flair and some time savers, but the only essential thing it adds is warframe or weapon slots.
