How to close off a mesh if there is a hole in it?

Hey everyone, I began using blender yesterday, it’s my first time. I’m really confused, lets say you delete a face on your mesh, how do you make a new one? I fixed it another way, but earlier I had this wierd spot where there was like two vertices lieing on top of each other and if I manipulated one, the other one would stay in the same spot and the mesh would get all wierd. I don’t know what caused it, but I could not figure out how to delete the mesh it self with out leaveing a hole in the mesh I could not fill in.

have you tried CTR+F?

No I have not, THanks!