Assembling Objects is a spatial skill, and the only thing that reliably improves it is volume. There is no formula to learn. Work through many puzzles rather than studying theory, and check the connection points before the overall shape.
Judging by overall shape
The wrong options are usually built to look roughly right at a glance. Check where the connecting lines actually attach to each piece. The attachment point is what separates the answer from the near-misses.
Rotating everything mentally at once
Take one distinctive piece and find it in each option. Eliminating on a single piece is far faster and more reliable than trying to assemble the whole thing in your head.
Spending too long on one item
The questions are short and roughly equal in value. If a puzzle resists for more than about twenty seconds, eliminate what you can, choose, and move on.
Improves steadily with practice and then plateaus. Two to three weeks gets most of it. Note it is not used by every branch — it matters most for Navy ratings, so check whether your target job uses it before investing time.