To place a gem into your Gear you need to unlock a Gem socket. Sockets are located in the Gear tab that can be accessed by tapping on a Sneaker or a Headset in your 'Inventory' tab.
Sneaker sockets can be unlocked after reaching the 15th, 20th, 25th and 30th levels.
Headset sockets can be unlocked after reaching the 15th and 30th levels.
To unlock a socket, you need to:
Open the 'Inventory' tab,
Tap on a Sneaker or a Headset,
Level up the Gear to at least the 15th level,
Tap on the 'Lock' in a heptagon icon,
Check the unlocking price at the bottom,
Confirm the unlock by pressing the 'Buy' button at the bottom of the screen.