Crafting... Hummm... Yes.
Let's see...
First thing you need is to collect materials in the Nebulas and exploration sectors. You know, those sectors where the "anomalies" appear, and when you get close to one, either it is a system with a mission to do in there, or a minigame.
The minigame rewards you with crafting materials.
Different sectors provide different materials, color-coded, and with three variants of it ( "atoms", "triangles" and "flowers" ). Each color marks the materials as appropriate for crafting items of a certain rank.
For instance, the red materials are suited for crafting Lieutenant level weapons and items. With red materials you can craft also certain items, like medikits, but the most important thing is that they are used to craft schematics.
Schematics are a vital part of the crafting process, as they are needed for everything. If you want to build a torpedo launcher, you will need a torpedo launcher schematic, and the same goes for a shield or a rifle, each of them has its own schematic. Also, schematics are not level dependant, so a shield schematic can be used for crafting a Mk VI shield, or the Aegis shield.
So, you can start by collecting as many red materials as you can, or as your patience allows. Collecting materials is booooring. Try to pile a few hundred red materials, and even then, you will be back to collecting red materials even when you get to VA.
The minigame for collecting materials will drop, from time to time, other materials, known as "particle traces". There are ten classes of them and when you get them all you will be awarded an accolade. Particle traces are also important, as they are needed for crafting the "good" items. All purple items need particle traces, different particle traces for different items.
Okay, so you have red materials. What now?
Assuming you haven't done so, fly to ESD, to the central junction. In there, there is a guy (don't remember his name) that will assign you the mission of going to Memory Alpha. Before doing so, though, it is a good idea to go to a food vendor (I think the ship replicator doesn't provide them) and get a "Bajoran Jumja stick". That piece of food is needed to complete a quest in MemAlpha, so having it ready will save you some travelling.
Go to Memory Alpha, (upper left corner of the Alpha Centauri sector block, if you don't know where it is), and land. First of all, complete the mission that brought you there, and look for more missions to do, several of them will give you some Diplomatic Points (DXP), and in some cases they are a basic tutorial for scanning anomalies and crafting.
Once done that, you can go to the central console, and do the crafting. You need to craft some schematics first, because they have no pre-requisite crafting points AND provide ten crafting points each.
So, select the "schematics" tab, look for the schematics of the items you want to craft, select it, and hit the "craft" button. Try to select useful schematics you plan to use: torpedo launcher schematics are a safe bet, but if you specced on cannons, crafting beam array schematics is wasting materials.
For the really nice items, you will need crafting experience, so crafting a few tens of schematics will give you a few hundred points of crafting experience. That should be enough for crafting Cmdr or LtCmdr level items, provided you have the proper colored materials, obviously. IF you don't have them, go to the appropriate sector and start collecting.
A useful trick when crafting is going from the items with lowest crafting points requirements to the highest. This way you are sure you have enough points for the hardest items. Still, be extra careful with the particle traces or you might find yourself out of particle traces for building the "really good" stuff.
You can also craft shuttles. There is a mission that rewards the schematics for the shuttle, which cannot be crafted, only obtained as reward.
