Delhi is a shopping center for goods from all over India, making it the best place to stock up on gifts and souvenirs. Bargaining is often appropriate—and almost mandatory. A good rule of thumb: When the price is written down, it's probably fixed. When you have to inquire about the price, it's negotiable.
In shops where foreign customers are uncommon, the staff is likely to follow your every move with great interest. If this bothers you, simply state your objective or emphasize that you're just looking; they'll cooperate if you indicate nicely that you don't need to be followed around.
Most shops are open six days a week, as each neighborhood's market area closes one day a week, usually Sunday, Monday, or Tuesday. Most shops in Old Delhi are closed on Sunday.