Can you activate a creature's tap ability the turn it enters the battlefield if it has haste?

Normally, a creature is subject to 'summoning sickness': you cannot attack with it or activate its tap (T) or untap (Q) abilities unless you have controlled it continuously since the beginning of your most recent turn. This rule is found in CR 302.6.

Haste (CR 702.10) is a keyword ability that specifically overrides this restriction. A creature with haste can attack and can activate abilities that include the tap or untap symbol in their cost the very turn it enters the battlefield under your control, regardless of how long you have controlled it.

It is important to note that haste only removes the summoning sickness restriction. All other normal requirements still apply — the creature must actually be untapped to pay a tap cost, and any other costs or timing restrictions on the ability must still be met (CR 702.10a).

Concrete example: You play Goblin Lackey (which has haste) on your turn. It has the ability '{T}: ...' You can immediately tap it to activate that ability the same turn it entered, because haste removes the summoning sickness restriction that would otherwise prevent this.

If the creature does not have haste, you must wait until the beginning of your next turn (having controlled it since then) before you can use its tap abilities, per CR 302.6.