On your Fight page, there's a bar that always displays Relics. They are always shown in one of two states, inactive and active.
Below is an example of what your relics look like with you have no relics (inactive). As you'll see, inactive relics are very dark with no color.
Below is an example of what your relics look like when you have relics (active). Any relic that you have will be bright and in full color. A timer will appear above it, which will count down how long you have left to use that relic.
As the timer is running the Relic is active and bestows upon you its specific enhancement for the entirety of the the time allotted. Once a relic's timer has depleted, you no longer receive its benefits and the relic will return to it's inactive state.
Note that occasionally you may need to refresh the Fight page to verify the different states. This can be done by using the F5 key on your Keyboard, pressing the refresh button on your browser, or by simply pressing the Fight tab on the page.