You target a permanent or player when the ability triggers. You decide whether to have Valakut deal damage to that permanent or player as the ability resolves.

If multiple Mountains enter under your control at the same time, Valakut's second ability could trigger that many times. Each ability takes into consideration the other Mountains that entered at the same time as the one that caused it to trigger.

If a Mountain you control leaves the battlefield between the time Valakut's second ability triggers and the time it resolves, be aware if that was the Mountain that caused Valakut's ability to trigger or not. If it was, Valakut's count isn't affected; if it wasn't, Valakut's count goes down by one.

Valakut, the Molten Pinnacle's triggered ability has an "intervening 'if' clause." That means (1) the ability won't trigger at all unless, at the time a Mountain enters under your control, you control five or more Mountains other than that new one, and (2) the ability will do nothing if you control fewer than five Mountains other than that new one by the time it resolves.