Summer plants: plant out after last frost in April or May.  
 
Melon plants are sold in 2.5-3" peat pots or plastic pots.  Peat pots can be planted directly in the ground, but I recommend tearing strips in the sides and bottom to allow roots to quickly grow into soil.
 
Space plants about 2 feet apart.  All melon varieties vine extensively.  Give them plenty of space, or allow them to crawl under established tall plants like okra, sunflowers, and corn.
 
Variety information:
Cantaloupe "Da Vinci": Very sweet, ribbed and netted cantaloupe that is quick to mature compared to other cantaloupes (70-80 days)
Watermelon "Sugar Baby": Produces small, "icebox" melons that are easier to manage for the home gardener.  Intensely sweet.  Red flesh.