I use Hodoku which has a "Vague Hint" command which is very useful I follow a certain algorithm for all puzzles. I'm sure other people do the same. Maybe slightly different near the bottom of the sequence when more advance techniques are required because I usually only do the ones I know. Right now I don't know all the advance techniques so maybe people have other strategies. But for most easy and medium puzzles I think people pretty much follow the same sequence. There is a group of techniques I call the 7 base techniques (steps 1 through 7).
Step 1: Look for any Naked Singles. If found repeat Step 1.
Step 2: Look for any Hidden Singles. If found go back to Step 1.
Step 3-7: Look for Naked Pair, Locked Candidates, Hidden Pairs or Naked Double, Naked Triples, X-Wing. If found go back to Step 1.
Step 8: Look for Hidden Triples. If found go back to Step 1.
Step 9: If there are cells with lots of pairs then look for W-Wings. If found go back to Step 1.
Step 10-17: Look for Skyscraper, Empty Rectangle, 2-String Kite, Remote Pair, XYZ-Wing, XY-Wing, Swordfish, and X-Chains. If found go back to Step 1.
Step 18: Use Hodoku's Vague Hint command to see if the puzzle requires a technique you don't know. (then learn it, come back, and try to solve).
Step 19: Go back to step 1
The order you look for the advance techniques is not as important I don't think based on my current experiences. Step 18 is important because you can use it to help you learn new stuff. Once you know what you need to know, you can go learn it and come back and solve the puzzle. This algorithm is the basic idea of a general puzzle solving strategy.
If you are interested here is a video I did using the algorithm above. I do the next step in the puzzle every 5 seconds and cycle through the list above as needed:
https://www.youtube.com/watch?v=JGqYjBiEE_8