See those two levers on the downtube just above where it says Olympic? They're the gear levers
Left is for the front - it changes between the two chainrings. Pull it back to go to the bigger ring (higher gear) push it forward to go to the smaller (lower gear).
Right lever is for the back, it changes between the sprockets on the back wheel. Pull it back to go to a bigger sprocket (lower gear) push it forward to go to a smaller sprocket (higher gear)
Think of the two chainrings as gear ranges. You'll change this less frequently. They aren't actually two distinct ranges because they overlap a lot, but that's the best way to think about them. Just keep it in the little ring (where it is) while you get going.
You have to be moving and pedalling when you change gear. Don't move the lever when stationary. When you do move a lever keep pedalling, but gently - slack off the power a bit.
I don't know if these levers are indexed (they will click between gears) or friction (they will move smoothly and you have to use judgement to find the right position). I'll assume they are friction, which is/was much more common.
So get on the bike pedal a bit to get going and gently pull back a bit on the right lever while pedalling gently. The chain will climb up a sprocket or two and pedalling will get easier. But maybe it will chatter a bit and not sound right, this is because you haven't got the lever in just the right position, so tweak it a bit,
It's a knack, but not difficult. Just roll around a park for a bit experimenting and you'll get the hang of it.