You need to have the running shoes, which are received at some point in the storyline of the region you are playing.
- Kanto: After beating Brock, head to Route 3 and Prof. Oak's Aide will give it to you.
- Hoenn: Mom will give it to you after you get the Pokedex.
- Unova: When you reach the route 2, Mom will meet you there and give it to you.
- Sinnoh: After picking your starter and fighting your rival, go back to Twinleaf Town and talk to Mom, she will give it to you.
The default key for running is holding B (mobile) or X (PC). If you changed your key binds, you can check the correct key on Settings > Control. You can also enable toggle run in Settings > Gameplay.