Shimmering Grotto isn't a creature, so you can tap it for mana on the turn you play it (this is no different from, say, Plains) (review C.R. 302.6).
(On the other hand, if a land becomes a creature the same turn it entered the battlefield, as with Inkmoth Nexus's second ability, it can't be tapped for mana on the same turn while it's a creature.)
(On the other hand, if a land becomes a creature the same turn it entered the battlefield, as with Inkmoth Nexus's second ability, it can't be tapped for mana on the same turn while it's a creature.)