How Do I Create A Member's Directory On My Site?

A little html and little php, good to go. I'm not sure what you want us to say.

If you want it to look almost exactly like the directory: google HTML elements and create lists of links

The search text could be done with a little php.

An organization I belong to uses the WP eMember plugin (WordPress) to manage the login privileges of apx 300 members. Very simple, I like it!

I don't know of a plugin off the top of my head that does that, but there are nearly 30,000 free plugins for WordPress, surely something will be close.

I always build custom plugins for the sites I work on, it is too much of a headache searching for something that ALMOST works, if only it had this little tweek. Then fighting with another's coding style and trying to learn how they did everything only to finally find out they forced a styling rule somewhere with an exclamation point that was completely overriding everything I did. So frustrating. I'd just rather build a plugin.

Yours seems like an easy enough project. I'll create one between the paid jobs I'm working on right now. It will be several months before I can get to it, so please look for another solution for the mean time.

Well, you'll probably want to create a database for it (e.g. MySQL/MariaDB or PostgreSQL). From there, you can use PHP to run the queries against it. It's standard fare stuff.