There are two tests for each brake. With the bike stationary, squeeze the levers hard to make sue that nothing is on the verge of breaking or has been mis-assembled. That test may seem silly but it reliably detects cables that are frayed to the point where they're dangerous, and also cheap shitty brakes (which will fail when you do this).
You can't effectively test braking power without having someone on the bike. The force required far exceeds most people's arm strength (could you catch someone thrown at you at 30kph?). So, jump on the bike and grab one brake then the other, rocking backwards and forwards while you do so. That tells you whether the brakes work at all. If they do, start riding, then tap the brakes as soon as you're moving enough to do that without falling off. Make sure you're riding somewhere that a: you can fall off safely and b: you can stop safely without using the brakes. The whole point of these tests is that they might fail. If you're confident the brakes work reasonably well, find a quiet street or carpark and do more of those tests, speeding up slightly each time.
A good bike shop will have someone other than the mechanic that worked on the bike do this test (and a bunch of other tests) after they service every bike. Once you've done it a few times it becomes fast and almost second nature. Swing a leg over the bike while holding the brakes firmly, rock it a little, tap the brake as soon as you're rolling. That helps avoid nasty surprises.
If you have a front disk brake and not a through axle, that first tap will also tell you whether the front wheel is seated firmly in the fork. It will do that by lifting out of the fork, so it pays to keep that in mind (yes, disk brake mounts were designed for through axles on motorbikes, then the design was copied straight to bicycles with no thought whatsoever. My bikes normally have the calliper on the right hand form blade, in front of the fork, so this can't happen)
Adjusting the brake depends on what sort of brake it is. Do a little research to find that out, then use the search box on the top right to find instructions for your brake (most likely it will be a V brake, but disk, calliper and cantilever brakes are all common too). Poor performance in the wet is normally a consequence of cheap brake pads, poor adjustment, or poor brake design (in that order, but you can suffer from all of those at once)