Use the vacuum's hose to vacuum over the entire baseball pennant. This will remove most of the loose dust that might be on the pennant's surface. Move the vacuum hose slowly and carefully, so you can remove as much dust as possible.
Attach the brush attachment to the end of the vacuum's hose. Very carefully, drag this along the surface of the baseball pennant, removing any dust that might be entangled in the fibers of wool and felt. For best results, do a spot test on the back of the baseball pennant, to make sure it can withstand the bristles of your vacuum's brush.
Fill the spray bottle with warm water. Lay the baseball pennant on a hard surface and spray it with water. Use the absorbent Sham Wow towel to soak up the dirty, dusty liquid from the pennant.
Hang the baseball pennant to dry in a room with indirect sunlight. Because a lot of baseball pennants can become collector's items, Don't hang them in direct sunlight, so you don't risk the images fading.