It's automatic
You don't press a button to Digivolve. Your Partner evolves the moment it reaches each level:
| Rookie | Lv.20 |
|---|---|
| Champion | Lv.40 |
| Ultimate | Lv.65 |
| Mega | Lv.90 |
Only Partners can Digivolve
Support, Buddy and SP Support Digimon cannot Digivolve, even if they're the same species as a Partner. See Which Digimon Can Digivolve.
Since Digivolution is tied to level, the key is leveling fast, which means selling gear from the Hologram Device.