Search for bugs, photograph them, and then identify them from the photos.
It can be a lot of fun hunting for bugs, but it's not particularly fair to catch them and put them in a glass jar. It would be much better to find the bugs, then photograph them, and leave them unharmed.
Where to look?
Anywhere were the ground is moist and shady. Gently part the weeds and see what you can find. Under a bark garden is another good place to look. The best place of all is a compost bin where grass clippings and vegetable peelings are put to rot.
Print your photograph and then try to identify the insects and bugs. You should be able to find a book in the library or on the internet.