In all cases, the arc move starts wherever the preceding move left off. You can't just program an arc as if it were a canned cycle. First you need a Rapid and/or Line move to bring the cutter to the starting point of the arc.
Then you have four choices for how to specify the arc, depending on what information you know:
EP&R = End point and radius. You know the coordinates of the end of the arc, and you know the arc radius. 95% of the time, this is what you want.
CP&EP = Center point and end point. You know the coordinates of the arc center, and you know the coordinates of the end point.
CP&A = Center point and angle. You know the coordinates of the arc center, and you know how many degrees you want to swing around that center.
3 Point = Three point arc. You know the arc starting coordinates (the place your previous rapid or line went to); you know some point midway along the arc; and you know the end point coordinates.
In each case, after you enter the information you know, Intercon calculates the remaining information. For example, if you enter an End Point and Radius arc, after you give the endpoint and radius, and choose CW or CCW, then Intercon calculates and fills in the center point and mid point coordinates, and the angle of swing.
Two things can be confusing on a Lathe. First, all your X axis coordinates are diameter values, and so are twice the actual distance from centerline. Second, CW/CCW is always judged looking at the "back" or "top" side of the part, as if X+ was up, even if your lathe happens to be assembled with the tool post in front of centerline, and your X+ jog button therefore pointing down.