Basically you have 21 speeds in 3 groups of 7.
The left shifter moves the chain around the 3 gears in the front where your pedals are attached. The right shifter moves the chain around the 7 gears in the back.

Basically you put the gears into which ever one you're comfortable with. The speeds means how fast you want the bike to go at a certain speed that you're pedaling at, meaning if you put it into the highest gears and want the bike to go fast, you have to pedal harder. If you put it into a low gear, it will go slow but also be easier to pedal.

For the front (left shifter): 1st = slow, 2nd = medium, 3rd = fast.
For the back (right shifter): 1st = slowest, 7 = fastest.

The speeds work in combinations. Think of it this way, the first number is for the left shifter, the 2nd number is for the right shifter. The speeds are as follows:
1-1 (slowest, 1st speed), 1-2, (2nd slowest, 2nd speed), 1-3, 1-4, 1-5, 1-6, 1-7 (speed #7).
Now you notice, by staying at 1st on the left shifter (thereby keeping your front gears on the smallest gear), you can only go up to speed #7. Put your left shifter in 2nd and now the speeds are as follows:
2-1 (speed #8), 2-2 (speed #9), 2-3...etc. 3rd is the same with 3-7 (speed #21) being the fastest.

Remember to only shift when you're moving, otherwise the chain gets all weird when you pedal. Try it in different combinations, no one can tell you what speed to use, it's what you're comfortable with.

I would start with 2-4. If you feel it's too easy to pedal and you find yourself pedaling too fast to maintain a certain speed then shift the right shifter up, if it's too hard shift down a few gears.

If you're going downhill and it's too easy to pedal even when you're at 2-7, shift the left shifter up to 3.

If you're going uphill and even 2-1 is too hard to pedal, shift the left shifter down to 1.

Just remember that by shifting the left shifter, you're jumping 7 speeds every time. To make the transition easier, instead of going from 2-7 to 3-7, shift down the right shifter to say 2-4 then shift the left up to 3. This helps make the transition easier so you don't suddenly find yourself 7 speeds up or down where it suddenly becomes too hard or too easy to pedal.

It's hard to describe and for you to visualize it unless you do it. Try practicing on the streets close to home when there aren't many cars around to see the effect shifting has. Just remember, higher numbers = faster but more work, lower numbers = slower but less work and then play around.

Worry about crossing gears and keeping the chain straight later after you're comfortable with changing gears.