Commonly you publish a link on your WordPress site that allows people to subscribe to an RSS feed. By default WordPress makes a feed url available at your domain name + /feed/.

So for example on this blog http://shilling.id.au the main feed is http://shilling.id.au/feed/

This functionality is part of WordPress, no plugins etc.. are required.

What is lessor known is that you can break this down and give a user the option to subscribe to an RSS feed that is just a category from you blog. You see this kind of functionality on news sites all the time, see the screen show here from smh.com.au for example.

This functionality is also built right into WordPress.

For example, on this blog there is a category of photographs available on this url:

http://www.shilling.id.au/category/photography/sydney/

An RSS feed is available of just this category simply by adding /feed/ to the end of this making it:

http://www.shilling.id.au/category/photography/sydney/feed/

All you have to do is work out which feeds are relevant for users to subscribe to individually and write some html to list them