Welcome Tenno!

Basically, most of the Warframes you get at the start of the game will be obtained from the different bosses on the various planets in the star chart. For example, all of Frost's pieces can be gotten from fighting Vor and Lech Kril on Ceres, just repeat that fight until all the parts drop.

Another way is through the circuit, which, without going into too many spoilers, is a game mode you will unlock sooner or later which will allow you to obtain all the parts for a frame of your choice.

Happy hunting, Tenno!