Unlike the situation with your 3-speed, this bike will permit you to accomplish the real goal of gearing, which is to maintain a nearly constant cadence of pedal rotation. Pick an "easy" gear to begin with, and count the number of times that your pedals spin (the same foot returning to the original position) in a 60 second period. When you have it in the 80-90 range, you're at the starting point.
Now work to maintain that cadence during your entire ride. You don't have to be going fast. Just let your body adjust to the feeling of this motion. Soon it will become the "natural" condition for riding, and you can progress from there.
Adjust the gears so that the same cadence results whether you're going up a hill, into a headwind, or rolling easily on level ground. As your body (muscles, heart, lungs) strengthen(s), you will be using a "harder" gear to accomplish the same cadence under the what previously had been more stressing conditions. Speed will improve accordingly. You're body won't know the difference, basically. Only your wristwatch will know that you've gotten faster.
Try it!
PG