Do I just go through sim>advanced>traits>change and just select 6th trait? Or do I need to add the sixth slot first somehow?

If you have UL you can use the social group or graduation trait slots.  MC>Sim>Advanced>Traits>Change Graduation Trait or Change Social Trait.  Otherwise, yes, I think you just add the trait with MC.  However, IIRC, it won't survive travel and/or maybe age transition.  I don't remember if additional traits will cause issues.  The Traits FAQ isn't up on the new site yet.  You might look for it on the Wayback Machine for more information.  You can increase the default number of traits per age group with Retuner.  See this FAQ and do a text search (CTRL+F with your browser) on the word 'trait'.

Adding a 6th or 7th trait by using Uni's graduation or social group slots doesn't cause any issues and they become permanent. Adding extra traits without using the Uni slots, or if one does not have Uni, only causes issues upon travel or aging up. It is best to remove the extra (non-slotted) traits before doing either, especially before a sim ages up, and then add them back in again afterwards to avoid errors. For general usage, the extra non-slotted traits are fine.

Mods from other sources that increase the number of slots are also fine as long as they are made or updated for current patch levels, but they aren't selective so everyone in town tends to end up with more traits as the extra slots get filled and this isn't always what the player wants.

How do I add the gratuated uni trait without going to uni though? Is there an option to do so without spending time at the uni?
I dont like social group influence so I rather not give them the influence if I dont have to.

KokosnootSpecerij, you can select 6-th and 7-th traits with Master Controller Cheats in advanced options menu (look TreyNutz post again) without spending time in university. Not needed add 6-th or 7-th slot first.

Giving a sim a graduation slot or social group slot trait has nothing to do with going to Uni or them having actual social group influence. Those are just the names of the "extra" slots and the 6th and 7th traits are provided by the player by way of MC rather than the sim earning them in-game. Not sure what happens when a sim who already has the grad trait actually does go to Uni and graduate, but I suspect the offer for a 6th trait just becomes meaningless at that time if it were to happen in much the same way that it does for sims who get more than one degree.

Oh I see, thanks for helping, everyone

You can also use the Honorary Degree LTR to give your sim the trait slot (and a degree).

If you want your sims to have extra traits and be applied to all sims automatically (random but can be changed), you can set up the number of traits for each age group in Retuner.  NRaas>Settings>General>by XML>Sims3.gameplay.ActorSystems>Trait Manager.  In there just add the number of traits you want each age group to have. I've set mine up to add an additional trait to each age group. You can add as many as you like. Hope that helps