There are two things you can do to improve a certain piece of armor or a weapon.
Since ESO has a really complex crafting system I will just provide some external links where everything is described In-Depth, otherwise this answer would probably be as long as the main script of the ESO main story...
1. - Enchant it!
You can Enchant a weapon/piece of armor by right clicking it and then use a glyph on it. If you right-click to enchant something you will automatically see whether or not you have a glyph that is compatible with your piece of armor/weapon. This will add a bonus effect. Usually it's + elemental damage for weapons and + Armor/Stamina/Health/Magicka etc. for armor.
Glyphs can be found in many places. You can buy them from enchanter NPCs, loot them or get them as rewards for quests. However the best thing to do is crafting them with the Enchanting skill (profession). To craft a glyph you need 3 different runes. Runes are usually just laying on the floor just like ore or wood but they can also sometimes be in chests and loot. The first rune (Triangle) will determine an enchants Level and whether it's a Upgrade of stats or a type of damage. The second rune (Square) will determine the effect of the glyph and the third one (Circle) will determine the quality (White - Orange). Note that the round ones are really hard to find so always make sure to collect them in the world (red runestones).
Just as an example I will show how a glyph is made:
You have the 3 runes Jora (Triangle), Dekeipa (Square) and Ta (Circle)
All 3 runes have a meaning.
Jora means Develop and determines the level
Dekeipa means Frost and determines the kind
Ta means Base and determines the quality
Now if you fuse those runes together you will get a rune of white quality for level 1-10 that grants you + Frost resistance. Note that if you change the rune Jora for The rune Jode you will not get a + resistance glyph but a + Frost damage glyph.
The whole enchanting thing seems a bit complicated at first but reading this guide should clarify things and while I highly recommend putting some effort into this profession I have to warn you that it is by far the most annoying one to level up. Runes are pretty hard to farm and they are popular.
2. - Upgrade the quality!
If you have the Material to upgrade an Items Quality you should do so. You can basically turn a home-made club into a legendary mace (It's just really expensive or risky...).
You can upgrade a Weapon by selecting the "Upgrade Item" tab at the respective crafting skill workbench. Then you will need at least 1 of the Items that are needed to upgrade the quality. You will get those by recycling Items with the desired quality (If you recycle a Purple item for example you can get a piece of crafting material to upgrade something to Purple quality). Keep in mind though that you won't always get one of said Items and that your Item has to be at the quality just before the one you want to upgrade it to. (If you wanna turn a White item into a Yellow one you can't just go White->Yellow but rather White->Green->Blue->Purple->Yellow).
Also you need a certain amount of upgrading material to succeed. While you can achieve it with one piece of each it's highly reccommendet that you try to get at least 80 if not 100% succession rate. If you don't succeed at upgrading an Item The Item and the materials will be lost
Upgrading the quality of an Item will result in more Damage/Armor, Value and The Perk on it will get better. The enchantment won't get better if you Enchant it yourself but it will be stronger if you upgrade an already enchanted Item.
For All the detailed information about Upgrading armor and Weapons take a look at this blacksmithing guide. While it only shows you stuff about the Blacksmithing perk you can basically apply it to every other Armor/Weapon profession by replacing the steel with leather or wood.
For some general crafting and improvement tips i'd recommend either the generic crafting guide of elderscrollsinfo or the crafting-simulator by ESOhead. In the crafting simulator you will see all the items you have to use for the different Armor/Weapon professions.