Gather Specimens isn't targeted. It affects creatures that would enter under any opponent's control.

Gather Specimens affects both token creatures and nontoken creatures. It affects creatures that would enter by any means. This includes, of course, creature spells that resolve. It also includes creatures put onto the battlefield as a result of a resolving spell (such as Call of the Herd or Zombify), resolving ability (such as Verdant Force's ability or Doomed Necromancer's ability), cost (such as Varchild's War-Riders's cumulative upkeep cost), replacement effect (such as the one created by Words of Wilding), or any other means.

If a creature spell controlled by an opponent would resolve, it resolves, but the creature enters under your control instead of the opponent's control. Choices made when casting that spell (such as whether it was kicked or the value of X in the spell's cost) are remembered. Any "enters" triggered abilities will trigger after the creature is on the battlefield under your control.

The Gather Specimens replacement effect is applied before any other replacement effects that would also modify how the creature enters. These are usually worded "as [this creature] enters" or "[this creature] enters with." For example, if your Gather Specimens has resolved, then the following things are true: -- If a creature with devour would enter under an opponent's control, you choose and sacrifice your creatures as it enters under your control. -- If Voice of All would enter under an opponent's control, you choose a color as it enters under your control. -- If Clone would enter under an opponent's control, you choose which creature it copies as it enters under your control. -- If a Wizard would enter under an opponent's control and that player controls Sage of Fables, the Wizard will not enter with a +1/+1 counter on it as it enters under your control. -- If a Wizard would enter under an opponent's control and you control Sage of Fables, the Wizard will enter with a +1/+1 counter on it as it enters under your control.

Gather Specimens won't retroactively change the control of creatures that have already entered that turn.

Some effects that put creatures onto the battlefield continue to affect those creatures later on. Although Gather Specimens changes whose control the creature enters under, the rest of the effect works as normal. For example, if your opponent activates a creature card's unearth ability and you cast Gather Specimens, that creature enters under your control, but the rest of the unearth ability is unchanged. The creature has haste. It's exiled at the beginning of the end step. If it would leave the battlefield, it's exiled instead of being put anywhere else.

If the effect that puts a creature onto the battlefield also creates a delayed triggered ability, Gather Specimens doesn't change who controls that ability. In the unearth example above, your opponent controls the ability that exiles the creature at the beginning of the end step. On the other hand, if the effect that puts a creature onto the battlefield grants a triggered ability to the creature (with "gains" or "has"), the player who controls the creature at the time the ability triggers will be the player who controls that ability. For example, if your opponent casts Makeshift Mannequin and you cast Gather Specimens in response, the creature will return to the battlefield under your control with a mannequin counter and it will have the ability "When this creature becomes the target of a spell or ability, sacrifice it." If the ability triggers, you'll control it, so you'll have to sacrifice the creature.

If two or more players have each cast Gather Specimens during the same turn and a creature would enter, the creature's would-be controller (the controller of the creature spell, for example) chooses one of the applicable Gather Specimens to apply. Then the new would-be controller of the creature repeats this process among the remaining Gather Specimens, and so on, until there are no more possible Gather Specimens effects to apply.

The above procedure means that if two opposing players have each cast Gather Specimens during the same turn and a creature would enter under the control of one of them, it really will enter under that player's control. (The creature would enter under player A's control, so player B's Gather Specimens affects it. Now that creature would enter under player B's control, so player A's Gather Specimens affects it. Each replacement effect has now been used, so the creature will enter under player A's control.)