Each of the tiers of resources have an equivalent set of Armor. These armors each have a set of Upgrades available to them.
Check which upgrades are available for the tools by looking at their tooltip while holding 'shift'.
To install upgrades, craft the appropriate upgrade item, and then place your armor and the upgrade item in a smithing table.
Use the upgrade templates to upgrade from one tier to the next, and maintain your installed upgrades.
Shift-Click any tool when it's in your hand to configure it. You can then click on your armor in this screen to access it's upgrades. From here, you can toggle on or off specific upgrades by clicking on them.
Right click the upgrade to change some settings (if they have any) or assign a hotkey. If the ability is passive, the hotkey will toggle its activation. If the ability is active, the hotkey will trigger it.
Active abilities, such as invulnerability, must be assigned to a hotkey. See the Upgrade Basics entry for more details on this system.
Armor can be upgraded in the smithing table (check JEI for the recipe) and will maintain installed upgrades when crafted in this way.