I give a shot, Left shifter is for the sprokets on the pedal arms, Right shifter the rear on the wheel.
Most flatland riding you only need to shift the rear, As Retro>G said start in the middle.
The biggest ring you shift with the left\ front gears on the pedals is for speed. The smallest is for big hills.

Why you have so many options is: THAT you do not want to cross chain, this means the chain is not straight.
The sprockets if you look are big to small front, and the opposite rear. The cog closest to the wheel\ rear is lange and in front opposite.

What does this have to do with crosschaining...well.

If you are going up\ down and flat you have to change the front derailler. What you attempt to do is avoid having the chain go from either one extream, large or small front, going to the opposte side cog rear.

If you only shift rear, staying on the middle front ring is best to avoid this.

Example to the extream, your large cog front,(outside ring) to easiest (largest) cog rear next to the tire. The chain is now not straigt, but running at an extream angle and your bikes unhappy.

You are to TRY to shift the chain straight as in the big ring to the first 3 rear cogs, middle front middle rear cogs and small (granny gear) is to run the last say 3 cog rear next to the wheel.

Some variation allowed, to much of an angle the shifting is poor, stretches the chain, shiftings hard.

Whew. Try flipping the bike over, or put in a stand, get your husband to turn the cranks and run the shifters.

Don't engage a shift while hard pedalling, you have to play clutch to some degree.

the hands knumb can be. Seat to high, seat too foreward, or perhaps entire posture is off. Generally its a seat hight\ distance.

Goodluck!
>Jef.