Ancient Greenwarden

Ancient Greenwarden's effect doesn't copy the triggered ability; it causes the ability to trigger twice. Any choices made as you put the ability onto the stack, such as modes and targets, are made separately for each instance of the ability. Any choices made on resolution, such as whether to put counters on a permanent, are also made individually.

An ability that triggers whenever you play a land won't trigger an additional time.

Replacement effects are unaffected by Ancient Greenwarden's third ability. This includes any abilities that apply "as [this land] enters the battlefield" and any ability that says the land enters the battlefield with counters.

Ancient Greenwarden doesn't allow you to activate abilities (such as cycling) of land cards in your graveyard.

Look at each permanent as it exists on the battlefield, taking into account continuous effects, to determine whether any triggered abilities will trigger multiple times. For example, if you control Ashaya, Soul of the Wild, a nontoken creature entering the battlefield will cause any appropriate abilities to trigger an additional time.

The trigger event doesn't have to specifically refer to "lands." For example, an ability that triggers "whenever a creature enters the battlefield under your control" would trigger twice if the entering land is also a creature.