First of all, I recommend using something with a big screen and a device that doesn't lag. I tend to use the computer. This helps me to spot more bugs than I would on an iPod(yes, some may argue I might as well zoom out) but it's too small for my liking. However, if it does work for you, zoom out to get a better view on your device if you aren't on a computer.
Back to catching bugs: I'll make a video showing how I catch bugs, and i'll try to explain it. But the only tip I could give now without a video is to leave bugs that you failed to catch, and ones are running away because you wouldn't be able to catch them, literally. If you see a bug, be a few steps away from it - then quickly approach it and press the action button.
It doesn't really require skill, more of catching it on the first go and leaving it if you do fail to catch the bug. Once the little buggers have ran off, you have no chance - so be quick. Position yourself, time it and catch.
Bug --- --- - -- Me (Run) (Catch)
I'll upload the video and demonstrate, hopefully giving you a better understanding. I'm sure other people have great tips to provide you. Good luck.