How can I refinish a Teek Wood shower stool. I sanded it. What next?

You can use tung oil. You can also use a marine poly. Good luck.

I assume that you mean a stool made of teak wood. That's a difficult problem for any wood finish. Waterlox makes a marine wood finish that is not cheap but I think that it would be your best choice for a long-lasting finish on teak.

Here is a great site that gives you instructions for caring for your teak bath bench!

http://www.aquateak.com/blog/teak-care-3-easy-steps-to-maintaining-your-teak-shower-chair/

How to get algae out of cracks in pavers

Teak Oil or Beeswax it.

For everyday use you should first rinse briefly with plain water to prevent soap buildup and then wipe any standing water off the surface of your teak shower bench and mat to increase the longevity of the wood and the finish.

You can use a marine grade varnish. It's water resistant and holds up well.

They do make a teak oil it could be that is all that is needed to give this piece a fresh look.