To add a player to your ignore list, enter the command /ignore <player name> in your chat window. To view/manage your ignore list, click on the EQII menu button in the bottom left corner of the screen, and select the "Community" menu from the drop down (Y default). 

To mute a player using EverQuest II's built-in voice chat, enter the command /voice mute.

How do I report a Community Standards violation in EverQuest II?