Heya,
I do a lot of insects. I have a few techniques. I do not use a flash. Ever. I use extension tubes ($50, Fotodiox Pro, has electric circuit for aperture control) on a 18-55mm EF-S cheap zoom lens. I do my shots both outdoors in natural sunlight, and indoors with constant lights (lamps).
Time of day: Insects are less likely to move much early in the morning. It's cooler temperature and they're going to be in a daze. If you move slowly, they won't even care that you're within 1~2" of them with a lens. During mid day when it's hot, they will scram before you're even within 4 feet. This simple knowledge will give you way more opportunities.
Understanding the bug: Some bugs move fast, some don't. Take a walk around your area where you want to shoot and see what kinds of bugs there even are there. This will help you understand what options you have. If you just run in circles after every single insect you see, you'll be missing the ones that are not moving and just watching you dance around. Don't chase flying insects. If you just casually go camp down in an area where the bugs keep swarming, like flowers, or a any food source, they will come to you naturally. They will be spooky of you first. But if you just hang out a while, they start caring that you're there and you can start getting shots.
Bait and/or Collect: I pick up dead insects. I find them under spider webs, cast away. I find them on the road, already rolled by a car. They are excellent subjects because they don't move ever. I take them inside, and pin them, and take photos with constant lamps. This lets me get my clearest images, with more control on focus and aperture for DOF since I don't do fancy stacking with a computer. Otherwise, bait your bugs. A little honey goes a long way! Dab some honey on some leaves or flowers or stems. Give it time. It will have guests showing up real fast. Works great for ants, flies, etc. Don't have honey? Mix some sugar in some water until it's real thick. Dab that on stuff. You'll attract bugs.
Move the camera, not the zoom: Set your zoom, if you have one. If using a prime lens, then just get it focused. On either lens, after you have it where you want it, focus it manually for your aperture setting for depth of field. Test this on any object until you get it just right for your shots. Once you have it, don't move it. Start just moving close to bugs and taking a shot. You focus by moving the camera, not the zoom. Practice this on a leaf in the sun or something. You'll figure out distances needed.
One last tip: You can get big grips to make it easier to hold the camera. I also use a shutter release remote, wired. It lets me hold the camera in one hand and move slowly, while holding the remote release with the other hand. This way I don't move the camera much when I take a photo, even when outside, because I'm not sacrificing grip stability when trying to hit the shutter button. The remote release helps me remove that and then I get more steady shots and I'm more likely to get my subject in the center of the lens.
Focus: Get used to not seeing your subject in the view finder, or on a screen. You can use a screen better if you're using one, but kiss your battery goodbye, and also note that in the sunlight if doing this outside, you're not seeing much anyways on those screens. Just get the idea of how far your lens needs to be from an object to get it in focus. Get some memory built up of that distance. Then simply move close to your subject and start snapping photos. Some of them will be keepers, some will be out of focus. If your'e inside, and you can see your screen, then by all means, focus properly and take your time. But in the field, you don't have that time usually and depending on the light or the bug, you may only have a second or two to really take some shots.
Very best,