I have a 20 yr old early American dining set. I would like to strip all the grease and dirt off and restain and finish with urethane. How best to obtain a pro finish?
First you need to deal with the dirt and grease. Use a strong cleaner, like TSP, Trisodium Phosphate, to remove as much grime as possible. This could raise the wood grain if there isn't much of a finish. Plus, don't be surprised if you need to wash more than once. Make sure to rinse the table really well after washing and allow it to dry for 24 hours before continuing.
Now, use a paint stripper to remove any remaining finish and even some stain. There are many different paint strippers on the market, some work and some not so well. It depends on what kind of finish is on your table. You might have to experiment a little. Follow the manufactures instructions.
The last thing to do is sand. This will remove any remaining stain/finish and get the table ready for staining. Use this article, <a href="https://www.house-painting-info.com/sanding-wood.html">Sanding Wood</a>, as inspiration. I recommend starting with a large vibrating sander and 120 grit, progress to 150 grit, then as much hand sanding as you can stand with 180 grit sand paper. Sanding sponges can be used on difficult areas.
Be careful with the sanding. If your table has a veneer instead of being solid then you can't sand that much. You don't want to sand through the veneer. In this case use the 150 grit then quickly progress to the 180 grit.