Crafting is handled via a dedicated screen called the Fixboy. It can be opened using the 'F' key. What items you can craft depends on the current Tech Progress of the Server. What Tier the Server is in and how far away it is from the next Tier, can be seen in the chat every time you log in. (In order to see it again, your character has to be logger out FULLY! That means waiting 3 minutes after logging off.)
Crafting takes Resources and Time.
While you can craft in your faction-base, it is generally not recommended to do so.
Not only will you have to pay double the amount of resources for current Tier weapons, you will also get lower quality items then if you would craft in the core, especially at an a Factory Interface, where you can only get Outstanding and Perfect Items.
Weapons & Armors can have up to 8 different Qualities. Perfect, Outstanding, Cool, Better, Normal, Bad, Very Bad, Garbage.
With each condition lower then Perfect, the Item will get 1 additional D-Mod (A negative Perk), as well as quicker Deterioriation to 0%. Each time you repair an Item, it has a chance to drop down a Quality. You can increase the quality again by repairing a Weapon that has already 100% Condition. This takes a huge amount of Resources however and is only viable for T+1 Weapons or Legendaries.
Your Engineering Skill has a chance to increase each time you Craft or Repair an item. The higher the Tier of an item, the higher the chance for it to increase. A higher Engineering Skill will help you craft better quality items.
Crafting at a Factory Interface will give you Outstanding or Perfect Quality Items, crafting at other Workbenches throughout the Wasteland will most likely wield you Better or Cool items. Take note, that crafting in base might cause you to spend double the resources. You can see if you need double the resources to craft an item at your faction base, if the numbers for the required Resources are Yellow. It is thus advised to craft in the core to not only save money but also get better Quality Items.
There are many crafting materials needed in order to craft items. Most of these crafting materials can be looted from the core. Some you have to buy from merchants or craft at Crafting Stations found throughout the Core.
The Online Map can help you greatly in finding those Crafting Stations.
Here's a list of current crafting materials :