Is it better to keep the air supply turned on the whole time i forge to keep it hot or turn it off when i get the steel out?

Think about everyone that uses hand cranked blowers or bellows, all through history, the air supply is only coming in when you operated it. This burns less fuel and as long as you don't take to long to get back to the fire it doesn't take long to get back up to heat.

Are you using solid fuel? and if so wot type? or a gasser,,,,? How long do you keep the steel out of the fire? Are you working with heavy stock or light?
Let me 'splain the questions, Some solid fuels will almost go out if you stop the air supply all together. Some not so much. if yoiu are using heavy stock that holds it heat longer then your forge will cool more and you may have to wait until the heat gets back up. Some gasseers use an air supply and some just use good ole shop air. Thin stock loses heat fast and a forge that is kept up to heat i sneeded. I use mostly gassers. When i remove stock i shut the fuel off and turn it back on for next heat. The gasser stay hot enough to light the fuel right up,i am old school in that the longer you keep the stock out of the heat the longer it takes to reheat. I know exactly wot I am going to do with the piece,,I do that and take another heat. Thta in mind the other question could have been how experienced are you in forging.......

I use charcoal. Thanks for the quick answer :D

Charcoal is a definite no; turn it off! If you have an electric blower keep an eye out for a foot switch that is only on when you stand on it---save lots of fuel and metal! (SOFA uses such a switch for their coal forges too, with an override for use with large stock or for forge welding billets.)

foot switch from a sewing machine should work