I'd recommend using a ready-made engine like OGRE 3D instead, but if you really want to reinvent the wheel, here's how...
In all cases I'm aware of, PC FPS games "trap" the pointer by registering a mouse motion callback, noting the relative motion, and then warping the pointer back to the center of the window.
Here's some code I wrote to add mouse input to a sample ping-pong table in an OpenGL with C++ course a year or two ago:
void resetPointer() {
glutWarpPointer(TABLE_X/2, TABLE_Y/2);
lastMousePos = TABLE_Y/2;
}
void mouseFunc(int sx, int sy) {
if (!started) { return; }
int vertMotion = lastMousePos - sy;
lastMousePos = sy;
player1.move(vertMotion);
// Keep the pointer from leaving the window.
if (fabs(TABLE_X/2 - sx) > 25 || fabs(TABLE_Y/2 - sy) > 25) {
resetPointer();
}
}
// This goes in with your "start new game" code if you want a menu
resetPointer();
glutSetCursor(GLUT_CURSOR_NONE);
glutPassiveMotionFunc(mouseFunc);
It only tracks vertical motion, but adding horizontal is trivial.