What is the best way to care for a popped blister?

TLC. Antibiotic ointment and a protective non-stick bandage (changed once or twice a day) for starters. Avoid any friction or rubbing on the area. If the area looks infected - weeping or draining fluid, or increasing tenderness, redness, or swelling, or other concerning symptoms - would be best to get an evaluation. Protect it from sun exposure.
Leave the skin on. If a blister pops and the skin is still present, leave it on. Blister fluid can actually deepen a burn, but the skin of the blister can act as a wonderful biologic dressing. Keep it clean and apply an antibiotic ointment and you will be just fine.
Keep it clean. A "popped blister" is similar to an abrasion & is not a deep inury usuallly. You mainly want to prevent complications such as infection while it heals. Gentle cleansing & keeping it moist with an ointment every day will help it heal without scarring. If it is in an area that is rubbed by clothing, keep it covered with a bandage to prevent further traumatization of the area until it is healed.