Bridges
Count neighbours first. An island with a number equal to twice its neighbours is complete: double bridges to all of them. An island one short of that gets at least one bridge to every neighbour.
Isolation. The finished map must be one connected group. So two 1s may not be joined to each other, two 2s may not share a double bridge, and any bridge that would cut a small group off from the rest is ruled out.
Look ahead one step. On hard grids, test a bridge: if adding it would leave a neighbour unable to reach its number, it is wrong. This is the only place where you look ahead, and it is always just one step.
Binary
Pairs and sandwiches. Two equal symbols next to each other are closed off by the opposite symbol on both sides. A single gap between two equal symbols takes the opposite one.
Count. A line that already has half of one symbol is completed with the other one. Check the rows and columns you have just touched after each move.
Finish lines carefully. With three cells left in a line, write out the possible endings; usually only one avoids three in a row. On the hard 10×10 grids, also compare nearly finished lines with complete ones: no two can be the same.
Lights
Chase down. Clear the grid row by row: for each light still on, press the one directly below it. The rows above stay dark.
Fix the top. What is left in the bottom row tells you which presses the top row needed. Make those presses and chase again.
Shorten. Pressing a light twice cancels out, so a solution is a set of presses. If your chase used a press and its repeat, drop both.
Practice
The puzzle packs go from easy to hard in each game. Work through the easy ones without the hint, then use the hint on the medium ones only when you are truly stuck: it always shows a step that can be proven, so it teaches the technique rather than just the answer.