The classic little book on the topic is South Bend's "How to Run A Lathe:"
There are many other books on the topic. About the only things that have changed substantially in the last 100 years are:
1. Tooling has progressed from high speed steel to carbides to insertable carbides (and insertable HSS).
2. Quick change toolposts, both the Aloris type and the Swiss Multifix type, are now much more common than the old "lantern" type of toolpost.
3. Higher RPM's. 100 years ago, you rarely saw a spindle speed above 1500 RPM. Today, there are manual lathes with 4,000 RPM max spindle speeds.
4. Coolant reservoirs. In Ye Olde Days, pork fat was used as cutting lube. Today, we have a variety of coolants and lubes, and having a pump and reservoir makes things go much easier on some materials.
Other than that, running a lathe is one of those timeless skills in a machine shop. If you can run a lathe, you might become a machinist. If you can't run a lathe, you'll never really be a machinist, no matter how many other machines you might be able to run.
The lathe is the granddaddy of all machine tools in the shop.