Before you get butterflies in your garden, you need to attract and foster caterpillars. The best way to do that is by providing them with foliage that they like to eat. For example, plant milkweed to attract caterpillars that will eventually turn into monarch butterflies.
This may seem a bit obvious, but don’t use chemically harsh insecticides on your garden. I know you want to treat for bad insects, but the insecticides can accidentally kill butterflies too. Instead, try a less harmful but still potent organic or natural insecticide.
Create a puddling area in your garden that will bring butterflies to your yard. A puddling area is pretty much a safe place the butterflies can go to get water and necessary minerals. What you do is put some sand or gravel in a shallow container and then add water. The butterflies will be attracted to it and come to your garden!
I also suggest leaving out pieces of fruit that the butterflies can feast on. You can spread them all around your garden or put them in one small area near the plants you want the butterflies to pollinate. The sugary syrups from the fruit attract the butterflies to your garden.
Talk to your local nursery and figure out what local plants you can grow to bring native butterflies. This is good on multiple levels. It encourages local growth and butterfly development, it makes gardening easier (since the plants are used to the climate), and it keeps gardening in the local sphere. This is like buying from the farmer’s market, but for your garden.
Make sure the plants you want pollinated are in full sun. Butterflies like to pollinate in the sun, so if your plants are in the sun, then they’re more likely to be pollinated. If you have potted plants, consider moving them in order to maximize on the sun.