If at all AE, complicated masking and distortion effects. This is not anything where someoen can "show you how it's done", it simply requires you to learn AE and the relevant workflows. Contrary to your assumption, this is rather advanced stuff and since it involves quite some manual labor, it requires patience. I'm sure you can find some "flowing paint" tutorials that give you a basic idea, but the specific process will be just that - lots of work.
When analyzing an effect you should start by looking at a few still frames and think in layers:
The flowing blob of paint is an additional layer added on top of the video. When the dancers move in front of the paint that's another layer usually created by duplicating the footage and Rotoscoping to remove the background. You don't roto all of the actor, only the part that goes in front of the paint so it may be just part of an arm for a few frames, then if the arm goes in front of the paint again a few seconds layer that's another layer.
The camera is moving so there is tracking involved. The technique can involve Camera Tracking, or planar tracking (mocha) or Motion Tracking (an area of detail, or Corner Pin Tracking, or Motion Stabilizing and then putting the motion back into the shot and adding it to the effect layers.
The paint was probably created in a 3D app using fluid simulation. To make the geometry match up you would use 3D tracking (different than Camera Tracking) to establish geometry for the wall and floor. You could also use Camera tracking or even motion or planar tracking and then math up the geometry by hand. If you were really patient and had a fair amount of time you could even match up the geometry by hand.
Then there is the texturing of the 3D fluid simulation, which is more layers but this time they are in the 3D app.
If you were really ambitious and wanted to create the paint layer completely inside AE using distortion effects you could also do that but there would be a bunch more layers and a lot of hand work.
An experienced crew could probably create this shot in a day. An amateur, working alone and learning as they go could easily spend a week getting the shot right. VFX and compositing is hard, requires pre-production planning and careful camera work to do efficiently, and requires an understanding of light, camera movement, perspective and parallax, lens distortion and a bunch of other things. Something like this will never be achieved by simply applying an effect to a layer and monkeying with the settings. To get an idea of how long it can take to create a single VFX sequence read this Tweet by my friend Stu. The shot could be done much quicker now but you'll get the idea of how complicated effects shots can get.