It's not too hard.
All you have to do is go to the homepage, click on User CP (above your avatar), then click on Group Memberships on the left. Tick the 'Join Group' box on the group of your choice, Partners N Crime in this case. Then click 'Join Group' at the bottom of the list. Next you'll be prompted to write a description of why you want to join. If you're already in PNC, that shouldn't be too hard. :P
When an owner of the group accepts your request, go to the bottom list of Group Memberships and tick the box next to Partners N Crime, titled 'Identify me as a member of this group'. Then click on Update Display Group and the title will appear there.
If you're an officer of the guild, you can apply for Partners N Crime Officers.
Hope that helps.