well if your problem is the theory behind it, maybe i can help a little bit.
First, quake3 patches use bezier curves, which are parametric equations. This means that to generate a point on the surface you need to input a parameter. The parameter can go from zero to one, and as it moves from zero to one the point generated moves along the curve from the start to the end. The parameter is usually called "t".
Second, quake3 patches use quadratic curves, not cubic curves (which are more common i think), so that means they have 3 points to define a curve instead of 4. The three points are startpoint, control point, endpoint.
Third, how to solve a quadratic curve? First, look at this picture:
P0,P1, and P2 are the three control points. Green stuff is intermediate calculations, and the red line is the final curve.
So to solve for the black point (a point on teh curve) you first find a point on the line from p0 to p1, call that A, then find a point on P1 to p2, call that B, then find a point on the (green) line from A to B, that point is your solution (black dot.) In all three cases, when you "find a point" you are finding the point using t -- if t is 0.5, find the halfway point. if t is 0.25, find the point 1 quarter of the way from the first point to the second point.
Okay, assuming you understand all that... the quake 3 patches are 2-dimentional surfaces, not just single lines. So instead of 3 points, they have 9. To solve it you need to do multiple tasks like the one above (solving a simple 3-point curve.) Since it's two-dimensional, to find a point you need two parameters instead of 1 -- instead of t, you need s & t.
Imagine the 9 points are arranged in a 3x3 grid. First row is 1,2,3, second row is 4,5,6, last row is 7,8,9. First solve three horizontal curves using s -- 123 is the first curve, 456 is the second curve, and 789 is the third. Each uses s as the input parameter. Each gives you one new point -- A,B,C. Now solve curve ABC with parameter t. Now you have found a point!
Okay, so now you can find any point on the surface of the patch using s,t coordinates. How to render a patch? What you do is divide the patch into a grid of quads. The vertexes of the quads are determined by inputting s & t. If you want N * M quads, you need (N+1) * (M+1) points. The first point is 0,0 and the last point is 1,1. Intermediate points are evenly spaced in between.