How do I get into this kind of faucet to fix a drip?
Note the manufacturer and google this repair giving the model and manufacturer; you should find information on this repair. Go to the home store and look for a repair kit for this manufacturer. Note that you must turn off the hot and cold supply to this faucet before you release the ring which holds the inner parts in place.

For example I Googled: youtube repair of single handle kitchen faucet and got this video https://www.youtube.com/watch?v=huxSQljCrIc