How you get your boost tokens will determine how they are given to you.
If you buy a boost token directly in the Shop with Super Cash, it is stored in your Inventory.
If you receive a boost token from a Shop package with other items, it is also stored in your Inventory.
You can find your Inventory next to the Shop button, in the bottom left of your screen. It looks like a golden boost token. You can then choose when you want to activate your boost - simply tap on it and confirm that you want to use it.
If you buy or win a Mystery Boost Ticket, it will be shown in the Shop in the Mystery Boost section. You will see the amount of tickets you own where the cost for the Mystery Boosts is normally shown.