Each of the tiers of resources have an equivalent set of tools. These tools 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 tool 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.
Activate or Deactivate the tool with the assigned hotkey ('v' by default). When the tool is deactivated, ALL abilities are turned off.
Shift-Click the tool when it's in your hand to configure it (there is also a hotkey for this screen). 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 the mob scanner, can be configured to happen either on right click, left click, or with a designated hotkey. See the Upgrade Basics entry for more details on this system.
Tools can be upgraded in the smithing table (check JEI for the recipe) and will maintain installed upgrades when crafted in this way.