Please note that this post has been rewriten to show the changs since the memmory alpha update from season 1.1 patch.
First things first. you must complete the mission "the egg". it starts from SB01 and directs you to deliver a special data sample (really just a quest item) to memmory alpha. report to commander romaine and then deposit the same as directed. After doing so, the crafting "store" will open to you. The consoles for accessing the crafting store are located in the center room called general R&D. There are also consoles in each of the profession rooms.
On your first look at the crafting store, you will see that the general R&D tab is open to you. each item listed under that tab has a number value next to it on the left. These numbers are like points, and you need to score 500 of them to unlock all of the tier 2 store. the tier 2 stores work in the same way, score enough points to unlock tier 3, except that the general R&D unlock effects all the professions for tier 2. Tier 3 stores are unlocked by scoring points in their respective tier 2 store and does not effect the other tier 3 unlocks, so science tier 2 effects science tier 3 only.
2 other things to note about memmory alpha.
1. when you have scored enough points in tier 2 and start wondering why none of tier 3 is unlocked. go to that profession's room and talk to the scientists there. FOR EACH profession, you must be given your first point to unlock the higher tier from one of the scientists. basically it's like a one time click quest to finish.
2. for the most part, it is not neccecary to farm or purchase the raw items needed for crafting. each profession's room has a vendor in it now. This vendor sells just about all items that can be crafted, except for the kits, I've not seen a vendor on memmory alpha that sells them.