What happens if a creature with trample is blocked by a creature that has protection from that creature's color?

Protection prevents damage from the protected source, but it does not remove the creature from combat or change how trample damage assignment works. When a trample creature is blocked, the attacker must still assign at least "lethal damage" to each blocker before assigning any excess to the defending player (CR 702.19b).

Here is the key interaction: when calculating how much damage is "lethal" for the blocking creature, the game uses the creature's toughness minus any damage already marked on it (CR 702.19c). The attacker assigns that amount to the blocker and can assign the remainder to the defending player. Protection then prevents all of that assigned damage from actually being dealt to the blocking creature (CR 702.16b), but the trampled-over damage to the player is unaffected.

So the blocker ends up taking no damage and will not be destroyed by that damage, but the defending player still receives the trample damage. Protection does not grant the blocker any ability to reduce the required lethal-damage assignment from the attacker's perspective.

Example: A 6/6 green trample creature attacks and is blocked by a 2/2 creature with protection from green. The attacker assigns 2 damage to the blocker and 4 damage to the defending player. Protection prevents the 2 damage to the blocker (it survives), but the defending player still takes 4 damage.

Note: Protection also prevents the blocker from being chosen as a blocker in some edge cases (CR 702.16d — "protection from [quality]" means it can't be blocked by sources of that quality... actually that's the reverse). To clarify: protection on the blocker does not stop it from blocking; it stops damage and other effects from the protected-against source from affecting the protected creature.