>how did I determine which form it will take on?

The form [Toxtricity][1] takes on is based on it's nature. 

- **Amped Form**:  Hardy, Brave, Adamant, Naughty, Docile, Impish, Lax, Hasty, Jolly, Naive, Rash, Sassy, or Quirky.
- **Lowkey Form**: Lonely, Bold, Relaxed, Timid, Serious, Modest, Mild, Quiet, Bashful, Calm, Gentle, or Careful.

If you want to choose which form Toxtricity will take on before you evolve it, you can [change Toxel's nature][2] in the Battle Tower. Due note though: If Toxtricity's nature is changed through this method, it will not change the form. 

>what are the differences between the two forms?

There are a few of differences between the two forms.

- Abilities: Low Key and Amped both get the abilities Punk Rock and Technician (hidden). The difference here is that Low Key gets the ability Minus whereas Amped gets the ability Plus.

- Moves: A majority of the move pool is the same, but there are some differences. Low Key Form can get the moves Venom Drench	and Magnetic Flux, but Amped Form cannot.  Amped Formed Venoshock and Shift Gear, but Low Key Form cannot

  [1]: https://bulbapedia.bulbagarden.net/wiki/Toxtricity_(Pok%C3%A9mon)
  [2]: https://www.serebii.net/swordshield/naturechanging.shtml