Because creatures you control enter as copies of Essence of the Wild, any "enters" triggered abilities printed on such creatures won't trigger.

If a creature such as Cryptoplasm that's already on the battlefield copies Essence of the Wild and modifies its own copy effect, that modification is also copied by creatures entering under your control.

External abilities may still affect how a creature enters. For example, if your opponent controls Urabrask the Hidden, which reads, in part, "Creatures your opponents control enter tapped," a creature entering under your control will be a tapped Essence of the Wild.

If a creature such as Clone is entering under your control, there will be two copy effects to apply: the creature's own and Essence of the Wild's. No matter what order these effects are applied, the creature will be a copy of Essence of the Wild when it enters.

Other "enters" replacement abilities printed on the creature entering won't be applied because the creature will already be Essence of the Wild at that point (and therefore it won't have those abilities). For example, a creature that normally enters tapped will enter as an untapped Essence of the Wild, and a creature that would normally enter with counters on it will enter as an Essence of the Wild with no counters.

Replacement effects that modify how a creature enters are applied in the following order: first control-changing effects (such as Gather Specimens), then copy effects (such as the abilities of Essence of the Wild and Clone), then all other effects. This is a minor rules change to make Essence of the Wild and similar cards in the future work intuitively.

If you control more than one Essence of the Wild, creatures you control will enter as a copy of the one whose copy effect you apply last.

Creatures you control don't copy whether Essence of the Wild is tapped or untapped, whether it has any counters on it or any Auras and Equipment attached to it, or any non-copy effects that have changed its power, toughness, types, color, or so on.