I garden organically and have very few problems with pests. The way to attract predators is by gardening organically, don't use any pesticides or herbicides, let the pests come and the predators will come along to deal with them. Also, don't be too tidy in your garden...leaf litter and patches of longer grass or a tangle of plants give the small creatures and bugs somewhere to live. Your pests give them something to eat and, if you leave out a bowl of water with some pebbles in (to stop the bugs drowning) I promise the predators will come.
The key is to holding your nerve when the pests arrive - just recently I had black fly on a plant and I really wanted to pick them off. I resisted and within a couple of days they were gone, something had come along and dealt with them.