You unlock drones after beating the bosses on level 10, 20, 30 & 40. You start with one drone.
To upgrade a drone you need geoms:
- level 2: 2500 geoms
- level 3: 3000 geoms
- level 4: 3500 geoms
- level 5: 4000 geoms
So you'll need 13 000 geoms to upgrade one drone.