Disconnect both battery terminals. Go and fill a deep-enough-pan with tap water. Place it on the stove and heat the water until it boils. ???
CAREFULLY take it to the car. CAREFULLY, insert each battery terminal in the boiling water for about 2 minutes. Longer if necessary.
The battery connectors will be as clean as new.
Then, CAREFULLY, pour the still-hot-water over the battery poles and everywhere you see the gunk... You'd be done in 5 minutes.
While you drink the Coke, you will see whether you really need new terminals

Vaseline has already been suggested. If you are picky, buy the two color-coded felt rings (Red / Green) made to absorb the battery gunk.
They're sold at any auto parts store for about $1.65. Those work well and look sanitary.

I do the suggested "Hot-Water-Drill" in all my cars every few months, even when they look clean.
