How do you unlock smithing? It's unlocked after the first boss fight in the story.

How does smithing work? You destroy three mods of the same type (weapon, ammo, elemental, armor, etc.) and rarity (white, blue, yellow, etc.) to get one mod of the same type and one rarity level higher (rarely two levels higher).

What level is the crafted mod? No matter what mods you spend, the crafted mod is always the highest level mod you can find. This means that you can turn early-game trash mods into end-game mods by smithing.

Is there any way to control the element of a crafted elemental mod? Yes. As far as I can tell, when crafting elemental mods only, the crafted mod will always have the element of one of the mods spent to create it. If you spent mods of more than one element, the crafted mod gets one of those elements at random.

Is there any way to control the other properties of the mod you craft? No. The properties of the mods you spend seem to have no relation to the mod you craft. (However, we may learn differently down the line; the fact that you can seemingly control the element of crafted mods suggests that the system may be more complex than it looks.)