In a Cessna 172 or similar, the flaps both create lift and slow the airplane down. The first notch creates a lot of lift and just a little drag. The third notch creates a lot of drag and a little extra lift. You can easily feel this in a full size aircraft, and the same principles apply to model aeroplanes.

In addition to creating lift and drag, flaps also stabilize the plane. With the flaps down, the wing produces more lift near the center (because of higher angle of attack). This means that the plane is less likely to drop a wing if you go too slow or pull too hard on the elevator. Stalls will be softer and more straight forward with flaps. Using flaps on takeoff, climbout and landing is generally "safer", unless you go way too slow with full flaps. There might not be enough engine power to recover.

When I fly models, I use the same procedure as when flying a full size small aeroplane: 1/3 flaps for takeoff, to create more lift and stabilize the plane. When to apply flaps for landing depends on how high I am. If I need to lose a lot of altitude, I might apply the flaps on downwind or even before that, to increase the sink rate. If it looks like I'm going to be short, I'll use only 1/3 or no flaps until I'm on short final, to make the plane glide better.

My rule of thumb is: 1/3 flaps for extra lift, full flaps for extra lift and brakes.

This is by no means the only way to use flaps, but it could be a good starting point. Different airplanes require different technique.