How does alpha blending work?

I''m writing my own software renderer currently and I''m stuck on alpha blending. I''m going to start by telling you what I can do, I can render a textured triangle with color modulated vertices. That is I can set the color of each vertex to RGB and it will blend the three vertices and texture beautifully. The formula I use is RGBn = (R1*R2, G1*G2, B1*B2) Though I''m stuck on how alpha blending works, how do I implement it?