The most basic aircraft today have what is known as the "6-pack". The 6-pack includes the Airspeed Indicator, Attitude Indicator(Artificial Horizion), Altimeter, Turn Coordinator, Heading Indicator, and the Vertical Speed Indicator. The hub of your instrument scan while flying is certainly the Attitude Indicator. It gives you nose up/nose down and bank angle information. It basically tells you if you are flying level. The reason it is also known as the artificial horizon is because it has a horizontal line in the middle, and the area above the horizontal line is blue(to represent the sky) and the area below the line is brown(to represent the ground). There is also a little shape in the middle of the instrument that represents your aircraft, and it shows you what your aircraft's position(attitude) is relative to the horizon.
Next, you have the Airspeed Indicator. You will notice it looks much like your car's speedometer. The only difference is that the airplane measures speed in knots(1.151 mph). On the airspeed indicator, there are all sorts of different coloured arcs and lines. The first arc you see is a white arc, and it is at the lowest speed. The bottom of the white arc is called "Vso" or stall speed in landing configuration(flaps down, gear down). The higher end of the white arc is called "Vfe" or your maximum flap extension speed. Next you have a green arc. The green arc is considered to be your aircraft's normal operating range. The lowest part of the green arc is called "Vs" which is the stall speed with your flaps retracted, and the landing gear retracted. The top of the green arc is your maximum structural cruising speed. At this speed, you can not be making tight turns or going through any kind of heavy turbulence, because you risk structural damage. The next arc is the yellow arc, which is known by pilots as the caution speed. In this arc, structural damage is a concern. The lower of the yellow arc is a line that meets the top of the green arc, which is max. structural cruising speed. At the top of the yellow arc is a red line. The red line is known as "Vne" or "never exceed speed". If you reach this line or pass it, there is a very high chance that structural damage is going to happen.
Next, is the Altimeter. The altimeter is a very basic instrument to read. It has numbers around the instrument from 0-9, and three hands. A large hand, a smaller hand, and the smallest hand. The smallest hand represents how many tens of thousands of feet up you are. The middle size hand represents thousands of feet, and the large hand represents hundreds of feet. What has to be taken into consideration, is that the altimeter gives you a reading according to how high above mean sea level you are, and not ground elevation. So precautions have to be made to make sure that you are clearing obstacles.
Next, we have the turn coordinator. The turn coordinator is simply an instrument to let you know obviously, if you are flying coordinated. It lets you know your aircraft's direction of bank, and whether you have the correct rudder input. There is a model of an airplane in the centre of this instrument, and it banks from side to side with your airplane, since it operates on a gyro. Underneath the model of an airplane is a ball in a tube with keroscene with two lines in the middle of the tube. If you are not flying coordinated, the ball will not be between the two lines. If the ball is to the right of the lines, you need to add more right rudder, if it is to the left, you need more left rudder.
The next instrument is the Heading Indicator. The heading indicator is a gyroscopic instrument that reacts instantly to your turn, and it does not have any turning, or acceleration errors like the compass does. The heading indicator is meant just to back up the compass, since the compass can be so difficult to read while you are trying to make a heading adjustment, due to these errors. The heading indicator has little marks every 5 degrees, larger marks every 10 degrees, and large bolded marks every 30 degrees. At every 30 degree increment are two numbers. These numbers represent in multiples of ten what heading you are on. For example if the top of the heading indicator reads "21", you are flying a heading of 210, which is southwest. At the beginning of the flight, you can calibrate your heading indicator to match your compass, and you should do so every fifteen minutes you are in level flight, since, because it is a gyroscopic instrument, it is vulnerable to errors due to gyroscopic precession.
The final instrument is the Vertical Speed Indicator. There is a needle that remains level when the aircraft is flying at a level altitude. Above and Below the centre of the instrument are marks that represent the aircraft's vertical speed in hundreds of feet per minute.
This is just a summary of how to use the "six-pack" in a conventional training aircraft. In larger commercial aircraft, there are things incorporated into the instruments to provide for almost no error, and to make things easier for the pilot. For example, in many large jet airliners, there are just three LCD screens that display the flight information. You see lots of other switches, knobs, etc in the cockpit to function various systems, but in these airliners, the flight information is displayed amongst three screens. Normally the FMS/EFIS, EICAS, and the NAV/COMM screens. That stands for flight management system/electronic flight instrument system, engine indicating and crew alerting system, and navigation/communication. On the FMS/EFIS, you have the entire six pack, and then some displayed all in one handy and collaborative screen which is quite simple to use. On the EICAS, you have the engine and system status for all operating systems in the aircraft, as well as fuel information. On the NAV screen, you have all of the information you need to shoot approaches, navigate the flight, talk to air traffic control etc.