Generally, you would not wear socks with climbing shoes unless you have a reason for it. Socks can help prevent chafing by providing an extra layer between your toes and the shoes. This could help in cases where you have new climbing shoes that are very tight or that you are not used to yet, or, you are a beginner climber, and you are not used to your climbing shoes yet. In these cases, the climbing shoes may be rubbing against your toes to the point where it actually breaks the skin and peels a thin layer off. Wearing socks can prevent this.
Other than this, though, it is usually preferred to not wear socks, since an important reason for climbing shoes being so tight is so that your foot will not slip inside of it or move around. Wearing socks can cause your foot to move around in your shoe, even in very tight climbing shoes. This can happen especially in the heel area and when you have difficult heel hooks where you really have to pull on your heel. Wearing socks can cause your shoes to not stay on as tight as they should, and could result in your foot slipping, the heel of the shoe coming off, and even in injuries if your foot slips in a risky way.
So the recommended way to wear climbing shoes is without socks. If you really want to, though, you can find a thin pair of socks to wear, just until your toes get used to the friction of the climbing shoes.
