Warframe is not a simple game by any stretch of imagination - this really cannot be stressed enough - but you can learn it by heart with a bit of time and dedication. One of the key components of the time you spend with this looter/shooter will be Relics, and here you will learn the what and how.
Firstly, you need to know that Warframe Relics will be your primary source of Prime parts and Formas, as these are the reward for cracking them open. Also, you'll get Relics by doing virtually anything and everything, but most of the good ones drop in Onslaught and high-level defence/survival missions.
The way to go about cracking Relics open is for you to check out the 'Fissures' tab in the upper right corner of your star chart UI. These are always on rotation and randomly selected from all the tilesets and missions that are available in the game, which keeps things fresher than one might expect.
There are four difficulty tiers of Fissure missions, each of which can be played to crack open a corresponding Relic. These range from the easiest (Lith) to potentially pretty difficult (Axi), and you'll have to select accordingly. By playing a Capture Fissure, for example, you will have to do the core objective, but with an added twist if you want to crack open your selected Relic.
Essentially, Fissures will keep spawning Corrupted enemies, who you'll have to take down and collect the Traces that they drop. Once you've collected ten Traces, your Relic will be cracked open, and you'll get a reward once the mission is completed.
The trick to efficient Prime farming is for you to play Fissures online instead of solo, because then you'll get to select from any of the rewards other players have received from their Relics as well, speeding your farming up exponentially. This way, you can get Prime items for free, or sell the parts to earn some Platinum!