as you will probably work out i am very new at electronics so please bear with me.
I have an AC transformer from an old soldering station. This transformer outputs AC current, 28v & 10 volts. I am trying to use this transformer to power up an arduino which i believe needs DC current. I happen to have 2W10 Full Bridge Rectifier. Would that be what's needed to get DC current?
Yeah, that and a filter capacitor. Keep in mind that 10VAC at low current draw will become close to 14VDC or thereabouts and the linear regulator on your arduino does not like that. So you'd have to add a DC-DC buck converter to step that 12-14VDC down to something safe for your Arduino; 5V would be a logical choice. Might as well get a small 5V switching power supply/phone charger and forego the whole soldering iron transformer in the first place...
I suggest you forget the old mains transformer and buy a modern power supply with 5V output.
I also suggest you start collecting power supplies from discarded electronic equipment and keep them to power your future projects, I have a ridiculous number of them, I will always have a power supply for any project.