Join the islands with straight bridges so each island has as many bridges as its number, nothing crosses, and every island is connected.
The full guide, with a worked example and common mistakes: How to play Bridges.
No — only straight across or straight down.
Yes. When the puzzle is finished you can travel from any island to any other along the bridges.
A simpler variant for younger players where two islands share at most one bridge. Numbers are then never bigger than 4.
Open the Bridges Solver, place each island and its number, and press Solve to step through every deduction.