I would also recommend linking your Warframe account with Steam. It can become a bother manually logging in twice every time.
All planets in Warframe have different materials to be obtained during missions. If you insist on not spending any money, you need to locate these and do missisons, planning ahead according to what materials you need.
Some materials may be exceedingly rare though, and evidently, you're gonna have to consult others for help with this.
You may have noticed this "Key" section here. It's a place where you will store extremely rare keys which you use to travel to special missions.
Warframe has loads of achievement. Some simple, some excruciatingly hard. If you want to get them all, you're gonna have to work for it.
To get help with more specific issues, theres also the in-game chat. When that don't work, try the newbie forum section.
If you wanna be the best, you're better off joining a clan. There's tons of leaderboards to help you decide which one is worth your time.
If there's something you missed in the tutorial, you can replay it here.
Evidently, all your efforts in this game will be to building a decent Warframe.
For beginners, I'd recommend looking long and hard in the store on descriptions. When you find something you fancy, check him/her out on youtube.
There's a constant stream of new warframes being released every other week or so. Zephyr here being the latest.
I would personally recommend the Rhino. Very straight-forward, sturdy and adaptable.
Weapons too can require significant testing.
As of right now, the Latron Prime is a very "OP" kind of Item, even with minimalistic amount of cards.
But alas, this concludes our guide over Warframe. Be careful spending too much on Platinum as only 3000 can cost a whopping 200$.
Have fun and goodluck fellow Tenno!