I think any wood worker will eventually gravitate towards wood turning. However wood lathes (good ones anyways) are expensive, this is my variant based on the ones from Grizzly, Vertilathe and Eccentric cubicle.
Step 1: Make a live center
The only thing you really need to do to create a lathe from your drill press is make a live center, and that's just a piece that holds the wood and rotates freely. Here's what I did.
I ripped apart an old battery drill, a cheap skil drill from the thrift store for a dollar, Out of the pieces you should be able to save a chuck with shaft and a thrust bushing.
Now bolt a scrap of hardwood to your drill press table and bore a hole through the wood slightly smaller than the shaft of the drill chuck. For example, the chuck shaft was slightly over 5/16th of an inch so I bored a 5/16ths inch hole. Here i'm using a scrap of Mahogany.