Prior to getting underway, you should implement an undocking plan with the help of your passengers. You should consider the direction of wind and current, the traffic in the area and the depth of the water.
Do not assume that everyone onboard has the same boating experience that you have. First, you can remind them that when boarding a small open boat, the safest way is to step into the center of the boat with a hand on the pier and one on the boat. Also, they can't read your mind so be specific and give direction if you ask for their help. Telling a passenger to attach a spring line means nothing if that person doesn't know the meaning of the term, which line to use and where (and how) to tie it.
Before launching from a dock:
Make sure to warm up your engines for a few minutes.
Also, check the oil pressure and other items on your pre-departure check list.
Wind or current is pushing your boat away from the dock
Cast off lines and pull in fenders as the wind blows you away.
When clear and safely away from the dock and other boats, shift to forward and depart at idle speed.
Be careful to make sure you have been pushed safely away and that the stern will not hit the dock as you motor forward and turn.
Remember: A boat does not steer like a car, it pivots on its axis at a point approximately one-third to one-fourth back from the bow when moving forward.
Wind or current is pushing your boat toward the dock (extra planning)
Cast off all lines except an after bow spring line. This line will keep you from moving forward and allow the stern to pivot away from the dock.
You may want to use a fender forward to cushion the bow of the boat against the dock.
Turn the motor or rudder to the direction necessary to push the stern away from the dock.
Shift into forward at idle speed. Slowly, very slowly.
The stern will swing away from the dock. When it is clear of all obstacles and traffic, cast off the spring line and back away from the dock.
When you are safely away, shift to forward and idle away from the dock.
Once you are clear of the dock, stow lines and fenders so they will not be in the way or pose a tripping hazard. Be sure to control speed when leaving the dock and check for other boats, swimmers or other obstacles.