An Anvil is used for crafting metal objects from base metal resources, such as Bronze and Iron. It is found in cities nearby trainers, often nearby resource fields and in buildable structures on player owned plots: Blacksmith Shop and Tinkering Shop.
Dragon Scalecraft can also be used with an Anvil, but won't get any skill bonus.
Anvils on player owned plots give a bonus to the related skills. The bonus is available for crafting purposes and is only shown in the creation window, not in the character skills window. If you are 75 skill points or less from being able to scribe a formula you can use these character shops to scribe as long as you follow the simple rule of using the creation window.
Example: You want to scribe the Expert Mining Pick (800 Metalworking) required. You are at 753 Metalworking. Simply act like your going to make another tool item that uses Metalworking, ie journeyman mining pick while standing next to the Expert Anvil, be careful not to have a tool in your hand it will limit skills. When the Creation Window opens you will notice a bump in skills by +75, boosting you to 828 at this point, leave the window open and open your inventory and then scribe the Expert Mining Pick formula.