The controller of the attacking creature chooses whether that creature fights Grothama.

If multiple creatures attack, each desired fight happens individually in the order the attacking players choose. Once Grothama has been defeated, any remaining attacking creatures can't fight it.

Creatures fight Grothama before blockers are declared. Any creatures that die in the fight can't be blocked. Any attacking creatures that survive the fight will still be attacking, may be blocked as normal, and will deal damage to the player or planeswalker they're attacking if unblocked.

Grothama's last ability triggers even if it dies without being fought by attacking creatures. For example, if you use Blaze to deal 10 damage to Grothama, you draw ten cards.