Upgrades are installed in Tools or Armor to grant them certain abilities. They can be installed using the Smithing Table, you should be able to look the recipe up with JEI.
There are several kinds of abilities.
Use Abilities are used to activate. For example, Mob Scanner is a use ability that when activated will show the position of all nearby mobs.
Passive Abilities affect how your tool operates. For example, the hammer ability allows your tool to break in a 3x3, 5x5, or 7x7 area whenever you mine a block.
Some abilities have cooldowns, like the invulnerability ability will make you invulnerable for a few seconds, but can't be used again for a few minutes. Both passive and active abilities can have cooldowns, but not all of them do. See the individual upgrade sections for more details.
Abilities can be controlled using the Tool Settings Screen which can be activated by shift-right clicking any tool.
Once in this screen, you can access the settings for other tools by clicking on them from the UI. For example, shift-right click a Ferricore Sword to open the UI, and then click on your Ferricore Helmet to access it's settings.
When looking at an item, you'll see an icon representing each of its abilities. You can left click this icon to toggle the ability on or off.
When off, the abilities won't activate by their hotkey if they are active, and won't cause their effects if passive.
For example, if you toggle off the hammer ability, your pickaxe will only mine 1 block.
Right click the ability to access it's options screen. For active abilities, you can specify which hotkey (or mouse click) activates them.
For passive abilities, the hotkey assignment will toggle it on or off when that hotkey is pressed.
Abilities can be activated or toggled even if the item isn't equipped! But first, toggle the 'activate if equipped' button to 'activate from inventory'
This means that you can activate the 'air burst' ability, or 'ore scanner' ability, even if the wand or pickaxe isn't in your hand. As long as its *somewhere* in your inventory, you can use these abilities.
Curios support is planned for some items.
Some abilities have custom settings as well. For example, the run speed or jump height abilities have sliders (available after Tier 2 armor), that control how much faster you run, or how much higher you jump.
Some abilities improve based on the tier of tool they are installed in. For example, the Hammer ability is 3x3 in a Blazegold Pickaxe, and 7x7 in Eclipse Alloy Pickaxe.