If you have ever hit your bow arm with the string, then you already know the value of an arm guard. Arm guards serve two basic purposes, protection to your forearm and making sure your clothing sleeves do not make contact with your bowstring. Serious consideration should only be given two these features since anything else is decorative and only considered if you want to color co-ordinate you archery equipment.
When you first start shooting you may choose extra protection and invest in a larger armguard that protects more of your arm. As you develop better form and become a more practiced archer you may choose a smaller style of armguard to better suit your level of comfort. There are tons of different types of arm guards on the market and they can be made with various types of materials including leather, synthetics and plastic.
Cartel provides a complete variety of armguards on their website to match any budget.
Jordan Sequillion 
I’ve used a heavy sock to protect my arm. It’s not as great as professional guards but it’s cheap and easy to get. You have to be careful though or a part of the sock (the heel typically) can hit the string.