Tier 1
Region completion
When a colour has one square left, the queen goes there. The simplest deduction in the game and the one that unlocks everything else.
Each colour holds exactly one queen. So when a region is down to a single uncrossed square, that square is the queen. No further thought required.
It sounds too simple to name, but it is the engine of every solve. You rarely find a region with one square by luck — you create one by crossing off squares elsewhere, then notice the consequence. That loop, eliminate then complete, is what solving Queens actually consists of.
Where to look first
Small regions. A region of two or three squares is one crossed square away from resolving, so scan the smallest colours after every placement. A region of twelve squares will not decide anything for a long while; ignore it until the board forces it.
This is also the reason boards with a wildly uneven region layout tend to be gentler than boards where every colour is the same size. Lopsided regions give you a foothold.
The trap
Beginners find the last square in a region, place the queen, and forget to run adjacency elimination on it. The new queen kills squares in three other regions and a row and a column; skip that and the next deduction stays invisible.