What can you do instead of using pesticides?

It depends on the pest you are trying to eradicate or chase away. Diatomacious Earth is organic and very effective on ants, earwigs, and several other pests. Insecticidal soap is also organic and very effective on aphids and other soft bodied insects, yet safe enough to ingest (not recommended, but it won't kill you). Slugs can be kept at bay with plastic or metal collars around the stem of your plant. 4 inch long popsicle sticks embedded at least 1 inch deep right beside the stem of your plant (no space between) will prevent cutworms from cutting off the plant (the cutworm must be able to completely encircle the stem to cut it, the stick prevents this).

Beneficial insects are also effective. There are parasitic wasps which can be attracted to, and sometimes purchased for, your yard. They kill many insect pests. Lady bugs can be attracted to, or purchased for your yard to keep aphids (their favorite prey) at bay.

There are many more ways to avoid using pesticides. I personally found the book Gardener to Gardener Almanac & Pest Control Primer, Edited by Vicki Mattern and Fern Marshall Bradley, and published by Rodale Inc. to be very helpful with such matters. Its ISBN is 0-87596-864-3.

The Organic Gardening link below might also prove useful to you, it has an extensive list of pests and organic methods of control.