How should I select front and rear gears?

Having more than one chainring (one of the front gears) expands the total gearing range available to you. Having multiple chainrings gives you a higher high gear for cruising at high speed as well as a lower low gear for spinning up hills.

The difference in the number of teeth between chainrings is much larger than the difference between sprockets in the rear. You can think of chainrings as being for major adjustments and sprockets for minor adjustments. You don't need to change gears in front nearly as often as in back.

The simplest gear changing strategy is to adjust the rear gears as needed and then change the front gears whenever you start to cross-chain. Cross-chaining is using the big chainring with a big sprocket or the small chainring with a small sprocket. It accelerates drivetrain wear and sometimes produces noise and grinding feeling.

My standard approach, and the approach I'd recommend for starting, is to use the front derailer to select a "range" -- big ring for flat road with no headwind, middle ring for slightly more challenging conditions (or riding in traffic), and small ring for serious uphill climbs. Then adjust the rear to select a comfortable gear within that range.

Or, if you're really unsure, just select the middle ring in front and only shift the front up/down if you notice that you need to.

As you gain more skill you'll notice that you can often, say, shift up in the front and down in the rear (or vice-versa) to achieve an "in-between" gear between two rear-only choices. But with modern bikes with 20+ speeds total this is not as important a "feature" as it was on old 15-speed bikes.