To connect vertices? I chose Vertex and tried to add a line by pressing F button. But if i connecting to another location,i creating a line that's out of the edge, just like in the picture. I thought my methods were wrong, but no one could fix them.

add I've added pictures, and I want to correct the fact that the lines in the middle don't apply at all.
I'm not quite sure what you are doing here, but it looks like you are trying to divide that n-gon up.

The knife tool is k, with it active click the first vertex, then the next.  This should result in the polygon being split along the resulting edge in the way you expect.