Does a triggered ability that says 'at the beginning of your upkeep' trigger on the turn you play the permanent?

A triggered ability that says 'at the beginning of your upkeep' uses the upkeep step as its trigger event (CR 603.2). The upkeep step occurs at the very start of your turn, before your draw step and main phase. If you play a permanent during your main phase, that upkeep step has already come and gone, so the ability has no opportunity to trigger this turn.

The ability will look for the trigger condition — the beginning of your upkeep — the next time that event occurs, which will be at the start of your NEXT turn. This is sometimes called 'missing a trigger cycle' by players, though technically it simply never had a chance to trigger (CR 603.3).

There is one nuance: if somehow a permanent entered the battlefield during your upkeep step itself (e.g., due to another triggered or activated ability resolving during upkeep), and the upkeep trigger checks 'at the beginning of your upkeep,' it would still miss because that trigger event is only checked at the moment the step begins, not continuously throughout it (CR 603.2, 502.1).

Example: You cast Howling Mine on your first main phase. When your next turn begins and your upkeep step starts, Howling Mine's 'at the beginning of each player's upkeep' ability triggers normally. But on the turn you cast it, that upkeep already passed — no trigger this turn.