I am unsure if you are interested in making a vegetable or flower garden, but you start either one the same way! Begin by marking the area you want to convert to a garden. Ideally, for veggies, you need sunshine at least 6 hours a day (for best yields). Less sunshine means less yield. For flowers, you can do sun or shade or a mix. Mark the area where you think you might want to create a bed using a rope or a really supple garden hose. Play with shapes. Make one, live with it a day or two, then change it as you desire. My two best tips are to start small (it's easy to get overwhelmed) and to make sure that if your bed has curves, that the lawnmower will easily roll around them (not too tight!).
Once you think you have an outline, mark the bed edge with flour, then begin slicing through existing soil with a sharp spade. Remove any sod, using it in a compost pile or to patch other bare spots in the lawn. Till in any soil amendments--get a soil test at the local county extension office so you know what to add (they'll tell you!).
Then start planting! I suggest looking at the garden plans on bhg.com. There are all kinds of plans for all kinds of gardens. Find one that looks good to you and that includes colors you like.
Get started as soon as you can this spring. Your timing is perfect! Happy gardening!