I just collected my brand new bike from the shop

OK, this bike has 3 x 7 gears and I cycled home comfortably using 2 and 1-7 as a combination. In the future, if I encounter a steeper hill or have a following wind on a straight stretch, what do I do with the rest?
I asked my husband: he looked the way he looks at MacDonald's when faced with ordering for a family of five via the intercom.
I asked my brother in law who said he had no idea.
I thought about asking my son but his idea of gear changing is standing up to pedal.
I thought about my daughter but her bike is asa rusted heap.
I tried Google and found somewhere that said that 21 gear bikes were actually only 13 gear as you can't use the full seven with each cog because the chain is too angled, but still I am puzzled.
Say I am cycling along and get to a hill and using 2 on the left and 1 on the right just won't get me up it easily. What do I do? Do I switch to 1 on the left handlebar and stay with 1 on the right? Or do I have to do something more tricky?
And if I am zooming along with 2 on the left and 7 on the right and what to go even faster, what do I do?
I've never understood bike gears. I would say bring back Sturmey-Archer but I doubt if I would like it if I did!