A small garden bed doesn't require loud or expensive power equipment to plow. You can break up the soil and get it ready for planting using nothing more than hand tools and a bit of sweat equity. A regular garden hoe, which sports a 6-inch blade affixed to the handle at a right angle, cuts into the soil and breaks it up so your new plants can send out healthy roots. Plow the garden in spring after the soil has dried out enough to work without causing compaction problems.
Dig a 3-inch-deep hole in the garden bed and gather a handful of soil. Squeeze the soil into a ball and drop it on a hard surface. Plow the soil if the ball breaks apart; if it splats or otherwise stays a single mass, the soil is still too wet to work.
Clear all large debris from the bed. Remove tree branches, large rocks and other debris that you can break up or till by hand.
Begin at one end of the bed. Grasp a wide-blade hoe handle in both hands, with one hand near the top of the handle and the other near the center of the handle. Bring the hoe blade down into the soil and pull it toward you, breaking up the top 4 to 6 inches of soil. Repeat the process, working backward, until you have plowed the row. Repeat for each row, working across the bed until the entire bed is plowed.
Cover the bed in compost, fertilizer or any other amendments necessary for the particular plant varieties you are growing. Plow the bed a second time, mixing these amendments into the loosened soil.
Smooth the soil surface with a metal rake before planting. Avoid walking on the surfaces you have plowed, because this will compact the soil again and make it difficult for seeds to germinate and roots to establish.