program that counts all the vertices in a given tree

I'm supposed to write a program that counts all the vertices in a given tree.

Any language can be used. (I've been using Perl mostly but could do C too. C++ would be ok too, if it was significantly easier.)

I'm not making much progress because I don't even know what the input is supposed to look like. Also, this seems like the kind of thing that there's a formula for.
-What does the input look like? (how is the tree entered into the program?) I've seen the graphical version. But how would that tree be typed in?
-I read if a tree has n levels, the number of vertices is 2^{n-1}. And for n edges, the vertices are (n-1). Maybe that will help.

I'm a grad student in electrical engineering but software is not my area of specialization. I didn't take the algorithms class. The problem would probably be simple to anyone who had taken the class. If you know a good reference book or website, I'd appreciate that too. Googling hasn't helped much.

For electronic circuits, I imagine the tree would be a Spice netlist.

The vertices are the nodes.

Thanks for your comments but I think this is the kind of tree I need to work with: https://en.wikipedia.org/wiki/Binary_tree