Presumably by tests. One factor is the temperature generated by the work. Since (on a lathe) it is a single point on the HSS tool, and a large area on the workpiece, heat tends to affect the tool more than the workpiece. So -- you determine what FPS (with which depth of cut) you can use without rising the temperature of the tool to a point which weakens it. Carbon steel loses its temper with relatively little heating. HSS can tolerate a lot more heat.
Other factors exist, such as whether the machine has enough horsepower to remove that much metal in that period of time, of course.
Note that there is not a magic speed above which everything falls apart and below which things are just fine. There is a range, and the published speeds are tailored for *production* work -- where it is cheaper to burn out the cutters a bit faster, just to get more work done in a given period of time.
For a hobbist, there is usually not the critical time element, and the savings of not having to purchase as many tool bits may make it worthwhile to run somewhat below the recommended speeds.
It is also possible to take too *light* a cut (at just about any speed). There is wear from the cutting, and a deeper cut means that there are fewer passes down the length of the workpiece, so you get more runs out of the tool before it needs resharpening or replacing.
To get *all* the answers probably would take a two or three volume book, but this is a start, at least.
Time for others to toss in their opinions now. (Nobody else had from the viewpoint of my news server when I started this response.)
Enjoy, DoN.