I have a question since I've never dealt with this before lol

My husband and I moved into a new apartment a few months ago, and it had a stove already installed. Like the one in the picture.

Well, my husband was trying to heat up some grease to fry chicken, and accidently spilt grease all over the stove, and it got in the eyes. I tried to clean it up, but I still can't cook anything stove top, because I guess I didn't get all of the grease out. And it smokes really bad, and I definitely don't want a grease fire.

I've never had a stove like this before, so I'm not sure what is OK to do to clean it? It's similar to the one in the pic.