Most of the time, when a card in play has a trigger, the triggered ability/effect goes on the stack and other things can be added to the stack as well. I know cards such as Land Tax either trigger or don't at the beginning of upkeep and nothing that is played after will alter whether it triggered (or didn't). But what about a cards such as Defense of the Heart? Does the sacrifice happen "immediately" when it triggers or does all that go on the stack (assuming my opponent has 3 or more creatures at the beginning of my upkeep)? And if so, could I cast Evacuation and then after that resolves, let Defense of the Heart's triggered effect resolve and put two creatures into play (assuming my opponent had 3 creatures or more in play at the beginning of my upkeep)? I'm sensing that I can'd to this because of the way Defense of the Heart is worded, but if that's the case, I'm wondering why it works differently than Land Tax.
In general, an ability of the form "At the beginning of [step or phase], if [condition], ..." triggers only at the beginning of the given step or phase and only if the given condition is true at that moment (C.R. 603.4, 603.2), and that ability will get to resolve only if that condition still holds upon resolving (C.R. 603.4, 608.2a). See also this thread. Certain choices have to be made when the ability goes on the stack, notably targets (see, e.g., Ana Sanctuary), but sacrificing a permanent is not one of them (no costs have to be paid to put a triggered ability on the stack) (C.R. 603.3, 603.3c-d, 601.2c-d).
Thus, if no opponent of yours controls three or more creatures by the time Defense of the Heart's ability (you control) would resolve, that ability does nothing (so that you don't sacrifice Defense of the Heart, search your library, etc.) (C.R. 608.2a). (A similar situation applies with Land Tax if no opponent of yours controls more lands than you by the time Land Tax's ability you control would resolve.) But if an opponent of yours does control three or more creatures when the Defense of the Heart ability would resolve, you follow that ability's instructions as much as you can (C.R. 608.2c, 101.3; see also C.R. 609.3), so that even if you no longer control Defense of the Heart when that ability resolves, you still search your library for two creature cards (and do the rest of the ability as much as possible) (C.R. 113.7a).
Thus, if no opponent of yours controls three or more creatures by the time Defense of the Heart's ability (you control) would resolve, that ability does nothing (so that you don't sacrifice Defense of the Heart, search your library, etc.) (C.R. 608.2a). (A similar situation applies with Land Tax if no opponent of yours controls more lands than you by the time Land Tax's ability you control would resolve.) But if an opponent of yours does control three or more creatures when the Defense of the Heart ability would resolve, you follow that ability's instructions as much as you can (C.R. 608.2c, 101.3; see also C.R. 609.3), so that even if you no longer control Defense of the Heart when that ability resolves, you still search your library for two creature cards (and do the rest of the ability as much as possible) (C.R. 113.7a).
EDIT (Aug. 24): Add rule citation.