The Augmentation system was introduced during the Lost Dungeons of Norrath(LDoN) expansion. Almost every single item can be Auged. What that means is putting a Augmentation into an item. To check to see if an item can be Auged right click and hold over it until the info window comes up. Towards the bottom of the window you'll see the following if it can be auged;
The item may have more or less slots depending on what item you have. Also Weapons will have a different Aug slot than Armor. Which takes me to my next topic, not all Augmentation's can fit into an Aug slot. Right click and hold on the aug, like you did to the armor to check to see what it's compatible with.
As you can see this aug is compatible with all races and classes. Below where it shows what races and classes it's compatible with it will show you what slots it can be put in. Below that is the stats of the aug and further down is what slot it can fit in. This aug says it fits in slot types: 7 (General: Group). What this means is it will fit in any type 7 (General: Group) slot. This is the most common slot found on any piece of armor.
Below where it shows what it can fit in is what Distiller must be used to remove it. The better the aug the more expensive the Distiller to remove it is. You can remove and put augs in, in the augmentation pond, which is more commonly referred to as the "Bird Bath". Below is a picture of it;
You can find bird baths at any LDoN camp in the Guild Hall and in the Guild Lobby. To put an aug in your item you need to place the item and the aug in the two available slots then click combine. To remove an aug you need to put the Distiller in one of the slots and your piece of armor.
Tribute was introduced during Gates of Discord. You can find your Tribute Master in your home city. Once you're in your home town use "find" to locate your Tribute Master. You can trade in items and plat to get Tribute Points. You can use Tribute points to buy temporary stat upgrades. The types of upgrades you can buy are Hp/Mana, Ac, Resists, and Hp/Mana regen. You can upgrade the buffs at any time by returning to the Tribute Master and spending more Tribute Points on a higher rank.
Tribute can be activated from anywhere. Once activated it will run for 10 minutes and cost you a certain amount of tribute points every 10 minutes or until turned off. For a list of all the buffs you can get from Tribute Points and every item you can turn in that gives you over 10,000 points click here.