Best way to clean this drain?

[agapoula19]

A few months of shaving cream, toothpaste, and my wife's luscious hair finally caught up to it. Even though it's not fully clogged yet, it's a very slow drain.
How should I get in there to clean it out? (Bathroom sink, two pics below)

 

[Geofd]

Under the sink were the pop up rod attaches to the drain there is a nut you remove that and it will allow you to remove the pop upon your drain usually a long pair of needle nose
Pliers will remove what ever is in the drain, ofr a plunger

 

[agapoula19]

Under the sink were the pop up rod attaches to the drain there is a nut you remove that and it will allow you to remove the pop upon your drain usually a long pair of needle nose
Pliers will remove what ever is in the drain, ofr a plunger

Thanks! I have this weird popup thing, I guess it's a new style, how do I remove it? (it doesn't even work...)