It is undoubtedly frustrating to loosen a screw and finding it too rusty and tight to remove quickly. When the screw is too tight, and you do not want to loosen, forget to remove it with a screwdriver first because the more screwdriver brand and more force you put is going to be useless.
First, if the screw is very hard, the ideal thing to do is to grab cola drink and apply it in the area where the screw is screwed to the material. Whether wood, metal or concrete several times in a day, use this gas and let the metal absorb it for 12 hours. Then try to remove it, it is very likely to come out without problems.
If the screwdriver still does not come out, it is ideal to put the screwdriver well and hammer it with small taps. It might be the vibrations of the blow that will remove it from the material where it is stuck. Try unscrewing the screw again to see if it loosened.
Still no loosening? It is time for us to attack with heavy weaponry. Go to the nearest hardware store and order an excellent screw loosening in the contact area of the screw with the material. Let it act for half an hour.
If it does not work, we little left to do, and that is to heat the screw.
This method is a little more radical and consists of removing the material around the screw, this damages quite a lot the area but is the definitive way to remove a rusty screw.
You need a torch, if you do not have one (it's not very common that there are torches in a house), you can try the flame of a candle for about 10 minutes. The heat dilates the metals which will cause the screw to inflate and detach from the material to which it is attached.
If it is still stuck, don't give up! There is only one play left to make. It consists of heating the screw for 10 minutes and then put a lot of ice on the area. The expansion by heat and subsequent compression of the materials will make a change in the structure by loosening the screw.