The attitude indicator (if your plane is equipped with one) shows you the plane’s attitude (angle) in relationship to an artificial horizon. This attitude corresponds to the angle your plane is flying relative to the real horizon. One of the skills you’ll be developing is learning the relationship between what the attitude indicator is telling you and what your eyes looking out over the plane’s nose and out the windows tell you.
Without an attitude indicator, you’ll use the nose attitude angle by looking at the outside horizon. You can also look left and right at the wingtips to determine a pitch angle. This is what instructors call “flying by the seat of your pants” and it’s fun!
For now, know that there is a specific speed and attitude for various types of climbs. If your engine is running at a specific speed and the plane is at a specified angle or attitude the aircraft is designed to climb (or descend) at a specified rate. So it’s very important that you know what this speed and attitude are so you can make your plane climb efficiently — and safely.
The normal climb speed and attitude for your aircraft is indicated in the aircraft’s operating handbook. Once you’re flying it’s too late to go look it up so make sure you know what it is. The normal climb speed is called the VY or best-rate-of-climb speed. There’s another speed for climbing when there is an obstacle (such as big trees or a building) at the end of the runway, called the VX or best-angle-of-climb speed.
Maintain the normal climb speed until the plane reaches about 500 ft. AGL or whatever number your instructor tells you. The altitude depends on what the traffic-pattern altitude is and what buildings and obstructions are near the runway. Some airports also require that you climb higher or make a slight turn to the left or right for noise-abatement.