There's more than one way to skin this cat.
First, the aforementioned center punch. You use a center head or similar method to roughly lay out the center of the shaft and then lay into it with a big old center punch and hammer until you have enough of a punch mark to use for a center. Put your part in the lathe and set the center into the punch mark and turn the shaft. Alternatively you can use the punch mark to start a center drill, insert the center, then turn the shaft. At this point you can try to turn the shaft complete, then spin it and attempt to get it centered while it's sticking way out there or you can spin it around, set up a steady and roll on the fresh turned surface and center the second end then finish turning. This is not the best method for a beginner.
Another way is to set the shaft up on a mill with the end of the shaft facing the spindle, then mill the end and center drill, reposition to the other end, mill that end and center drill. Then move the part to the lathe and start turning.
One more: make an end cap with centering set screws and a center in the end or use a live chuck in the tailstock to cut spots on the OD for the steady rest. Set up the steady and run on the spots, then face and center the first end. Spin the part around and face and center the second end. Remove the steady and turn the shaft.