export data from 1.3.7 to 1.5.1

I have a client with an active site using 1.3.7 with very little modification. I want to test what he has in categories and products by exporting the categories and products data in 1.3.7 and importing into 1.5.1. Need some guidelines on the procedures. Thanks

Simple.
Assuming you have a clean copy of v1.5.1 installed:

1. export entire 1.3.7 database
2. import it into your v1.5.1 database, which will replace your entire temporary v1.5.1 site data with the old site's data
3. run zc_install in your v1.5.1 site to upgrade the database to the new structure

Don't do a selective copy of just categories and products. While doing a selective extraction of data might sound shorter, it's actually more complicated and prone to problems.

I'm not mentioning addon accessories like EasyPopulate because apparently those aren't already part of your workflow so probably don't suit.

Besides, I suspect that your question is a precursor to planning a proper upgrade ... and a proper upgrade SHOULD NEVER BE just an extraction of cats/prods from an old site to a new one. So, giving you an exact answer to the exact words you used would be a disservice to you and take you down the wrong path.
Ref: http://www.zen-cart.com/entry.php?3-How-do-I-rebuild-my-site-on-the-new-version-instead-of-upgrading