Jan is an official first name. It is not used by friends and family. They use either Janek or Jaś. I use the latter. The relation between Jaś and Jan is like between Jimmy and James. Some people find "Jaś" too informal, and they use "Janek", which is slightly more formal.
The last letter in "Jaś" is an "s" with a sort of an accute accent over it. "ś" has no corresponding English sound; it is much softer than "sh". "J" in Jan and Jaś is pronounced like "y" in "yellow".
I have already given up efforts to teach foreigners how to pronounce and spell my first name. Sometimes those efforts had unexpected results: they stopped calling me by my first name. Had they also known, that in Polish, one uses vocative case when calling someone... Dutch people call me Jan, and it is also both official and familiar Dutch first name, and I'm happy with that. It is pronounce slightly differently in Dutch ("a" is different), but I noticed that after 2.5 years of hearing my name pronounced in that way, so it does not really matter.