Welcome! Concerning your lathe - do you mind sharing which lathe you have? Knowing this can help considerably.
A problem that recently came up is one from long ago. I hope this does not get too technical. IF you don't understand, please ask for clarification.
Wood lathes usually come with a tail stock live center ( the opposite end from the head of the lathe). The tail stock live center on WOOD lathes are made for turning
wood. (of course) However, many people use a (metal rod)
mandrel for turning pens (some of us do not). IF you use a
mandrel, the tail stock end of the mandrel has a small dimple in the end. The Live center point fits into the end of the mandrel. This is where the problem starts. The WOOD lathe live center is not meant to fit into the Mandrel. It "will" but they do not match perfectly. Soon there will be a minor but "wobble" developing. You will need a 60° live center (ordered from one of several places.) The wobble will introduce an Out Of Round (OOR) pen blank. Not by much but enough to be noticeable. (BTW, OOR is technically incorrect, but sufficient for description.)
Practice: One great help is to order 20 or 30 tubes and drill holes in them and practice different aspects of pen turning. Practice using the chisels, scrapers, skews. Find out which one is best for you. Practice turning to size and don't worry if you turn it down too much (this IS practice); Practice sanding and different grits of sand paper, practice applying finish until you develop a "feel". Practice Drilling the blanks. Get use to it. Find out what tools you may need down the road.
IF you have a Harbor Freight store near you, they have metal calipers on sale about every other month for about $10.00 Don't buy composite ones but metal ones. Learn to use the calipers for measuring the size. Measure the center band, the nib end, the clip end and mark them down on a piece of paper. Turn and measure, turn and measure; when close to size, sand down to the correct size. But MEASURE with calipers.
Sandpaper, some people treat pens as they would furniture and start off with 120, go to 180 and 220 grit. I never start off with less than 400 and move up from there. This is the importance of turning and measuring. You CAN use sandpaper to sand it down, but that is what the chisel tool is for. With practice and skill, sandpaper will be used for final smoothing and not for sizing.
CA, (or superglue) is the primary choice of finish although many other finishes are used by different ones. Practice with CA. A caveat with CA: CA fumes can cause allergies to develop and sudden flu like symptoms develop within hours. I use CA on most of my pens, but I became severely allergic to it about 2 years after I started using it. Now I use a respirator and face mask ALL the time.
An OLD and somewhat out of date PDF on getting started:
http://content.penturners.org/library/general_reference/Getting_started_in_pen_turning.pdf
(some terminology is out of date)
Here is a link to a thread in which I asked what people had wished they had known earlier:
http://www.penturners.org/forum/f14/if-i-had-known-earlier-46654/
That is kind of a long read but it is helpful.
