Prune tomato plants early in the morning on a dry day. This helps the plant heal properly and reduces the chance of infection. Don't prune any plant that is less than 1 or 2 feet tall, or it may not recover from the shock.
Once the plant is the appropriate size for pruning, it has branches coming out of the stem. Where the branches meet, there is an additional branch growing, called a tomato sucker. Use a clean, sharp pair of shears to cut off these sucker branches. After pruning, water the plants at soil level to prevent splashing on the plant wounds.