Edge the garden for a tidy appearance and to show the lawn the line it is forbidden to cross over. Perhaps it will stay on its own side. This can be as simple as laying down newspaper and covering it with straw or wood chips, or as complicated as laying bricks. Make paths at least 3 feet wide. Dig the soil by hand or with a rotary tiller.
Many gardeners use a technique called double digging, described in most general gardening books.
Add any amendments recommended in your soil test. For example, limestone will remedy acidic soil and agricultural sulfur with neutralize alkaline soil. Plant seeds and plants according to packet or plant-stake directions or the recommendations in standard references. Water the plants thoroughly, and celebrate.