The left hand is required to run a lot of tasks while playing the guitar, and classical repertoire in particular makes hefty demands. For this reason it is important to set up your left hand correctly right from the beginning of your development. If you establish a solid foundation then you will put yourself in the best position to improve and develop quickly.
Many pieces written for classical guitar require a lot of independence in the fingers. For example, your index finger might be holding down one note while your middle and ring fingers play a short scale. Because the fingers need to do so much moving around we need to make sure that our hand position allows for that movement to happen with as much ease as possible.
If you were to hold the guitar on your lap, with the guitar neck parallel to the floor, then the wrist would have to be at an angle in order give your fingers access to all the frets. This angle might work for a little while but soon enough you will find that the left wrist starts getting tired. Bending the wrist means that the pulley system of muscles and tendons in your hand will get damaged over time, much like a climbers rope that gets torn from rubbing on a cliff ledge.
So, in order to keep the wrist in a more ergonomic position, we can raise the guitar neck on an angle that allows us to have more access to the fingerboard without straining our wrist. The angle of the neck will differ from player to player depending on height, the type of chair and guitar support being used. In general, the headstock of the guitar will be at eye-level with the player. For more on this check out the sitting position.
To set up your default left hand position, relax your arm and hand completely, let it flop towards the floor. Then bring the arm up towards the neck, moving from your elbow, and let the fingers lay gently on the strings around the first few frets. From this relaxed placement, curl your fingers so that 1, 2, 3 and 4 occupy frets 1 through 4 respectively on the 3rd string. The thumb will live in the middle of the neck, which is approximately where your fingers will be placed on the third string.
Rule of thumb…
The most common tendency for beginners is to let the thumb poke over the top of the fingerboard and grip on as if you were going to dangle from there for a while. This is quite a common position for some guitarists who play other styles of music or perhaps who play guitars with a slimmer neck. On electric guitars, the neck can be so slim that players will actually hold down notes on the bass strings with their thumb! On the classical guitar we are always aiming to give the fingers as much access to the fingerboard with the least amount of tension. By gripping the fingerboard with the thumb we limit the reach of our fingers and we also make it more difficult to leave the treble strings ringing clear because the skin from the base of the fingers can often touch the string, which stops the note from sounding clearly.
So, in order to have the fingers hop around freely on the fingerboard the thumb will live around the center of the neck. It can move around quite a lot and even though at the beginning of your studies you might feel the need to squeeze with the thumb to get notes sounding clear, over time you will learn to use the thumb more for a guide in shifts and to stabilize the hand. Squeezing the thumb against the neck will make your hand feel tired until you develop a more refined sense of weight and touch in the left hand.