How to equip artifacts?
In order to equip an artifact, select the champion that you want to equip the artifact on. Then double click on them in the portion of the window where you see the parties health bars at the bottom of the screen. This will bring up the unit menu.
In the unit menu you can use the up/down arrows that you see to scroll through artifacts to equip. Double click on an artifact to see what it does. When you find one you want to equip, click and drag the artifact into the hand of the champion.