Might of Atlantis is on a very short cooldown for an ultimate ability, so don't be afraid to use it whenever it is available. Remember however, you need to hit with an ability for Might of Atlantis to become usable. Both Surge and Wrath can be used on drones and monsters, and Capsize does not need a target at all.
Wrath's ability description in-game is self-contradictory, but it seems to scale with percentage of missing health. Since it can be used on jungle creatures, using it when a powerful creature is at low health can be very effective.
Might of Atlantis "remembers" the last skill you used before it comes available. For example, if you hit a target with Trident of the King 1 second before Might of Atlantis finishes its cooldown, it will be immediately available for 3 seconds the moment it comes off cooldown. Same goes for learning the skill.
Since Undertow's range is quite short and can only be used a second time if it hits an enemy, try to dash towards an enemy drone when escaping, or when chasing an enemy champion just out of range.
Trident of the King -> Surge could be used as an escape. Trident of the King can hit and mark jungle creatures you did not have sight of, and Surge allows you to dash through walls. Also note that Surge has a much larger range (estimated 1850) than Trident of the King, allowing you to further mislead your opponents with your movements during the 4 seconds, or to easily catch up with enemy champions who use escape abilities after being marked by telepathy.
Stagger and Wrath does not have to be used on the same target.
While Undertow needs to hit a target to unlock Capsize, Capsize does not need a target and has a longer range, but it doesn't seem to be able to dash through walls.
Trident of the King has great range, decent damage and a low cooldown. Its range is long enough to hit targets just behind a turret from outside its range, although its missile speed is fairly slow.
Might of Atlantis will activate Rising Tide. Both uses of Undertow will activate it and Rising Tide does not stack, so try to use a basic attack between them.
Rising Tide will activate regardless of whether the skill hits a target.
The second use of Undertow does not require Will. The cooldown only starts after the second use.
Attacking structures will not consume Rising Tide.