I have not studied celestial mechanics, but I believe I know enough about the basic priniciples to answer your question.

Suppose you and the ISS are in coplanar circular orbits around the earth and you want to dock with it. To minimize fuel consumption, you should need to do this via an elliptical transfer orbit with appropriate apigee (high) and perigee (low) points. To enter the transfer orbit, you would need to use your thruster briefly to increase your speed to that for the transfer orbit just as you reach the transfer orbit. The transfer orbit would need to cross the ISS's orbit just as the ISS was passing the crossing point, On reaching the ISS's orbit, you would need to use the thruster again to decrease your speed to match the speed of the ISS. Identifying the appropriate time and thrust for entering the transfer orbit and the approprirate thrust to use in leaving it would be laborious without use of a computer.