Finding the First Bridges
Compare each island with its neighbors: a 5 with three neighbors must send at least one bridge to each of them, since two neighbors can give it at most four. A 1 next to a single neighbor sends its only bridge there. These sure bridges cut the paths of others, and the puzzle opens from them.
The Connection Rule in Practice
At Medium, watch the small groups: two 1s cannot link to each other, and two 2s cannot share a double bridge, because each pair would be cut off from the rest. Ruling those bridges out often decides where the remaining ones must go.
The Classic Hashi Size
The 9x9 puzzles balance length and clarity: enough islands for real deductions, few enough that the page stays easy to read. Start with Easy, then move up one level at a time.