Every Linkshell group has one Master of the Linkshell. It is usually the person that created the Linkshell group, but it is possible for a Master to reassign Master status to someone else via options on the Linkshell list.

If you are not the Master of the Linkshell, you can remove yourself from the group with options that are available with a right-click on the list of Linkshells you have.

If you are the Master of the Linkshell and want to get out of the group without blowing the whole group away, you need to reassign Master status to someone that is staying in the Linkshell group, and then remove yourself from the group with the options available on the Linkshell list.

If you are the Master of the Linkshell and want to completely get rid of the entire group, you can talk to any of the NPC's that can create a new Linkshell. Those same NPC's also have an option to completely get rid of an existing Linkshell group.