Linkshells and how they work?

I am still fairly new and I've only heard of linkshells in passing.

Can anyone explain how they work and how I would go about finding them on my server?

It's a form of group chat that most people use to share information quickly with others who are interested in similar activities. Typically you can find some recruiting on the world specific forums others advertise in shouts or party finder. I'm sure there are other ways to find them but this is all I really know myself.

Linkshells are essentially chat channels, often with a specific purpose.

They're less of a commitment then a Free Company, but it's a way to keep in contact with like-minded people.

Popular kinds of Linkshells include Hunt Linkshells, focused on relaying information about locations of Hunt Marks in the open world
FC alliances, intended to facilitate cooperation between FC's and for filling in parts for any dungeneering/raids that happen
Static Coil LSes, as a dedicated chat channel for static groups whenever you're not in a party
And just general chat channels.

You can be in multiple linkshells at a same time. Just remember which one is which so you don't sound completely silly when talking into the wrong one!