When you salvage an item it turns into either a design or an essence (there's no way to control which, it's random)
There's a big random element to this but generally the better the item, the better the des/ess you'll get, but again this can vary a lot and there's a huge random element to it
When salvaging, the item is completely destroyed and there's no going back, so don't salvage anything you want to use/keep
When you want to improve an item you have, use the combination window in your bag, like you combine runes. Add the item you want to improve, along with one design (of the right type) and one essence. If it successfully crafts, then it will go red and you can use an ID scroll on it to reveal new stats
Sockets and mythics will stay, but all other stats and orbs will be reset and re-rolled
Essences and designs have 3 numbers associated with them. The top number (quality/volume) is closely related to the number stars the item you salvaged had, the higher the better generally. The middle number (detail/purity) is closely related to the level of the item salvaged, there's a lot of debate around this one but the general consensus is to use ess and des that are about the same or slightly higher than the level of the item you are crafting. The third number (slag/fade) you want as low as possible, although the exact function of this is still a topic of debate
Crafting can be an expensive hobby, some of the best items in the game have taken hundreds of re-rolls to get to where they are, so it's often cheaper to just buy things that already have stats you like
There's also a strong market for designs and essences. If you have decent level things with high stars it can often be worth salvaging and selling the des/ess that you get, as you may get more than you would from selling the item to shops
Have a browse through AH to get a feel for the prices they sell for, the stats on the des/ess make a huge difference to the value, so pay close attention to that when browsing
Hope this was helpful to you!