How to care for my wound and dressing after abscess drainage?

As instructed . After an incision and drainage of an abscess follow all post procedure instructions exactly. If anything is unclear call te physician or surgeon who treated you for this problem.
See you doctor. Wound care instructions should be obtained from a physician who has inspected your wound. Not all wounds are the same and not all will have the same treatment. Generally however the wound the site should regularly be cleansed with sterile saline or a wound cleanser. Deeper more involved wounds with signs of infection may require oral antibiotics. Consult with your physician.
Abscess care. Your surgeon should be giving you instructions on the care of the abscess.
Simple Care. The real question is what not to do that slows down healing. Avoid using alcohol, peroxide, hibiclens, betadine, and bleach solutions. Inflammation ( red, hot, swollen, tender) is important to healing so anti-inflammatories (motrin, advil) are bad. Cover the area with a clean dressing changed every other day and protected from trauma. Antibiotics do not help healing unless it is truly infected.
Call your doctor. It is hard to answer this question without knowing more information. Simple abscess soap water antibiotic ointment keep it covered. Complicated abscess needs different treatment. Do you need antibiotics by mouth IV etc. Call the doctor who did the procedure.
Ask. Best to ask your doctor or surgeon. Usually daily cleaning with soap and water after removing the bandage, packing the opening with new clean gauze is indicated.