I hope that almost all of this is self-explanatory.
The 'S' in Spivak is supposed to stand for 'simple'.

0. Downloading

The program is distributed in a disk image (.dmg) file. Save the .dmg to disk; double click to open it, then drag the application to your desktop, or Applications folder.

1. Entering formulas

The three wide fields at the top, center of the window are the components of the parametrization. The formula parser knows the following functions: sin cos tan sinh cosh tanh arcsin arccos arctan arcsinh arccosh arctanh exp ln and the following binary operations, with their usual precedence: + - * / ^ You can refer to the constants pi and e by name in your formulas. Use 'u' and 'v' for your parameters; other variable names will be treated as if they are zero.

2. Choosing a point (and direction)

Click and drag in the upper left ('domain') window to choose a point in the (u,v) plane, and you'll see the corresponding point marked on the surface in the main window. To choose a direction (for a geodesic, or tangent line), Control-click in the domain window. You'll mark a green reference point, and the implied direction vector is from the white point toward the green point. You can also use the vertical slider at the far right of the screen to change the direction vector.

3. Adjusting the view

You can click and drag in the main window to rotate the view, and you can Control-click-and-drag to zoom in and out. The small slider on the right controls the size of any decorations you're currently drawing.

4. Writing the rest of the documentation

This is currently happening.