You have a forge in every major city. In Whiterun (I assume it is the 1st city you start in), there are 2 : On right at the entrance, on the right, another before going up the stairs leading to the keep, on the right, you have a big yellow building, on its left, some stairs going up to another forge (the Skyforge, the most reknown forge in the area).
You need to begin forging easy stuff with Iron. There are several iron sources. You can go mining around (the biggest iron mine is west of Whiterun, defended by some bandits) by using a pitch on iron veins, then transforming your iron into ingots, then use these ingots and leather to build easy stuff. This will raise your Smithing skill.
You can also buy iron ingot directly at blacksmith and their shop.
To build advanced stuff, spend points you earn at each level into smithing perks. You'll see the Smithing tree has 2 branches, right and left. Right branch is more about heavy armor, left branch more about light armor, chose appropriately.
You can do it in a normal fashion, building stuff now and then when you have the iron at hand, or power your way up the Smithing skill by forging tons and tons of daggers, getting iron as soon as you can (vendors replenish every 2 days), going as far as traveling constantly from 1 city to another to have constant vendors and iron sources to constantly forge things. Less "roleplay" and may break the immersion factor, but you get the smithing done way earlier. Again, your taste, your choice
