In Elliptic Curve Addition, where does the second point come from? I have a limited understanding of elliptic curve terminology, but if you can bear with me I'd like to ask this question anyway. I'll start with what I understand...


You do EC multiplication with the private key to get the public key.
EC Multiplication is just EC Addition (done over and over again).
EC Multiplication can be achieved through a combination of EC Addition and EC Double (for speed).


From the perspective of the graph:


EC Double = draw a tangent on your current point, take the intersect, invert it.
EC Addition = draw a line through your current point and a second point, take the intersect, invert it.


EC Double I understand -- you have your current point and you draw a tangent -- no need for any extra points on the curve to get the intersect. 

But in EC Addition, if I have my current point, where does the second point on the curve come from when attempting to draw a line across the graph to find the next intersect?
In elliptic curve cryptography, participants need to agree on certain parameters. For example, you need to agree on which curve to use.

One of those parameters is called the base point generator, it is a point on the curve.


  You do EC multiplication with the private key to get the public key


Correct, PubKey = PrivKey*G = G+G+G+... PrivKey times where G is the agreed-upon generator. Does this clarify things?

You can see its definition in SEC 2 in section 2.7.1.