As I posted noticed you updated with pictures. That's some good corrosion going on there.
To clean a terminal isn't that hard. They sell battery terminal brushes that will do it and some sprays that will break it down and clean, but if you don't want to spend money you can use a toothbrush, baking soda and water.
A good instruction set I've followed:
- Remove the ground connection first by removing the negative (-) terminal from the post (note: older vehicles may have a positive ground)
- Remove the positive (+) terminal from the post
- Scrub any corrosion off the terminals, cables and posts using a stiff brush
- For tough buildup, use a solution of baking soda and water, taking special care that none gets inside the battery
- Dry it off with clean cloth
- Reconnect the terminals in the reverse order from which you removed them, positive (+) first, then negative (-)
- Double-check to make sure the connections are tight and secure