Weapons in skyim have a base damage rating. The higher this number is, the more damage it will do. Armour has a base armour rating. the higher this number is the less damage you will take. Keep in mind that standard armour that is not enchanted will only resist physical attacks. Armour rating will not resist magic attacks no matter how high it is. leveling and spending skill points in smithing will enable you to craft and upgrade weapons and armour to a higher rating than regular weapons and armour found throughout the world. An important thing to note is that in the smithing skill tree there is two perk directions you can take. The left side will most benefit light armour builds and the right side will most benefit heavy armour builds.
To craft either weapons or armour use any forge you can find. This list shows all the types of armour and weapons that can currently be crafted. Select the type you want then find the item you wish to craft. Below the item it shows the materials you need to craft that item. The number in brackets shows the amount of that material you have. If the requirements are met then that item may be crafted. Notice that crafting the item will gain you experience in the smithing skill. If you lack the required items the easiest way to obtain them is to purchase them from a blacksmith, provided you have the coin. All major town forges will have a blacksmith who sells smithing materials. If they are not selling what you are after, wait 48 hours for them to restock or try another blacksmith.
You can also find materials throughout the world. Find a pickaxe to mine rocks for various ore. Hunt animals for pelts and hide to turn into leather. And keep an eye out for ingots, ore and certain scrap metals laying about the place. Once the materials are gathered and the item is crafted, for armour use the workbench to improve your armour rating. For weapons use the grindstone to improve the the damage rating.
You will notice that the improved item will then gain a quality status. As your smithing skill level increases armour and weapons will be able to be improved to higher levels. Legendary being the highest. The higher level the item is the better armour or damage rating it will have. Without leveling smithing these levels are much harder to obtain. Keep an eye out for amulets and rings that enable weapons and armour to be improved further. This may just put your weapon into the next level tier.
if you have animal hide. Use the tanning rack to turn them into leather and leather strips and if you have some ore. Use the smelter to turn the ore into ingots. Leather leather strips and ingots are the most common crafting materials. Finally a tip for leveling your smithing early on is to craft iron daggers as they take the least materials to craft. They can then be sold back to the blacksmith.
And if you need some extra coins check out the jewellery section. Craft jewellery to sell for a good amount of coin. This concludes my guide to understanding smithing.