The first step to getting a great finish on your turned vessel begins with the finish off the gouge and skew. Tool marks, tearout, and excessive sanding are a detriment to [any] great finish and must be avoided.
Begin sanding at 220 grit and finish with 320/340 grit; sanding in an oscillating manner by hand. Be sure to have a pliable backing (foam or the like) on your sandpaper to avoid finger grooves in the wood. If you use a power-sander, come back and sand by hand to remove the burnished surface created by power sanding at 320/340 grit.
After sanding with the 320/340 paper, soak the vessel with Boiled Linseed Oil (BLO) and do one final sanding with 320/340 grit, then remove any of the slurry created with a cotton cloth and Denatured Alcohol (DNA).
This step will leave the vessel surface feeling silky smooth, and also highlight any flaws in the wood that will require your direct attention to remedy.
Now, let the BLO cure (which will depend on your shop environment) and denib with 400 grit paper, if needed, before moving on.
Continuing, Polymerized Tung Oil from Watco or Minwax are the oils I use, but other brands are available.
This Tung Oil application system requires 2 steps. Step (1) uses dilute Tung Oil 60/40 with denatured alcohol (60% DNA, 40% Tung Oil), step (2) uses 100% Tung Oil.
I find it best to use a small, quality (Sch 2) plastic container to transfer a small quantity of Tung Oil for the application processes to limit the amount of open time of the master container. This will greatly increase the longevity of all your finishing oils if you do this.
To apply the Tung Oil, I use 2″ x 2″ squares of napkin. Rags or t-shirts leave lint on the surfaces.
The steps are:
Step 1: In the first couple of coats, apply the 60/40 mix in a thin coat, this will wick into any of the open grain pores. Two coats work best for this. Allow time for the oil to cure. Once the second coat is dry, denib as required for any dust or fibers.
Step 2: Apply full strength Polymerized Tung Oil. Using a 2″ x 2″ napkin, apply a thin coat of oil to the surface, being careful to not saturate or introduce air bubbles into the oil. You can apply in any grain direction, but you must ensure you
finish the application by pulling the oil with the direction of the grain. As the oil builds, swirls going against the grain will stand out. Allow each coat to dry based on your environment.
Between coats, you may need to denib air bubbles or dust accumulation. To remove, spray with water and wet sand with 1500/2000 grit black paper.
If the surface is gummy, the prior coat was not dry. DNA (or acetone) and a cotton towel will take this off with some elbow grease.
Apply as many coats as needed to achieve your desired luster. Depth of shine can depend on the type of wood and the number of coats applied.
Wet sand with 5000 grit black paper or a 8000/12000 grit micro mesh pad to knock off any fuzzies. Be sure to spray with water; only the fuzz will be removed while leaving an unblemished finish.
Finally, buff with a high thread count cotton towel.
