It's a couple of different phenomena, all at the same time. Let's start with the most accessible. Your hand out the car window.

Flat hand, you feel a pressure at the front of your hand. At the back you should notice is a bit dry.

The pressure at the front is dynamic pressure. The gas piles up as your hand plows into it at speed. The pressure you feel is the mass of air you're picking up and carrying with you. The dryness at the back (you don't feel it per se, but you can notice it) is the resulting area of low pressure created by you plowing through the air. This is drag.

Now. Tilt your hand in the stream, and up your hand will go! The ways you can break this down/visualize it are varied, but in reality are all manifestations of the same phenomena.

Newtonian/Conservation of Energy: Each particle of air impacting the bottom of your hand is +1, each impacting the top is -1. +1 & -1 don't neutralize, so up you go.

The vacuum visualization: imagine a density visualization overlaid on the situation. There's a vacuum bubble over the top of your the hand. Nature hates a vacuum, so everything tries to fill it. The end result of that filling, is that air particles that would otherwise be slamming into the top of your hand get "sucked" into the bubble instead. This is important, because without this understanding, you can't account for things like dumping energy into the flow stream via a spinning shaft or the infamous UFO X-plane, where all the engine power was devoted to keeping air flowing faster over the top surface, allowing the darn thing to get lifted by the relatively unaccelerated air beneath even at 0 velocity of the machine relative to the environment. The key to all lift is making that asymmetry in airflow.

Symmetric airfoils can create lift at Angle of Attack, because while they are symmetric at 0 degrees, they aren't at angles offset from dead on.

There are also some weird degeneracies that you can take advantage of, like using a spinning cylinder and flat strip of material just barely offset from it to create lift with near zero relative forward speed of the apparatus to the surrounding space. (This is a function of viscosity, and the energy of the spinning rod is basically picking up the fluid and accelerating it, it separates from the cylinder and follows the strip of material creating a pressure differential, ergo lift).

Then there is the whole bit about about vortex circulation etc, the main thing to remember though is that air that is trying to fill a void created by an object moving through the air is too busy doing that to neutralize the energy gained by air transferring energy to the bottom of the lifting surface. Ergo, lift. Further, the useful "lift" you make, the more "drag" you'll create as well, because in order to maintain that vacuum you're coaxing all that air on the topside of the lifting surface to head into instead, you have to account for the energy expended in 'picking up and carrying' that air/fluid with you.

Fluid dynamics is weird, complicated, and seems like black magic, but at the end of the day it's all about what you convince the fluid to do instead of smacking into you.

There are gobs of seriously bloody weird equations all around it, but they are mostly useless in terms of being able to visualize what is going on.

Imagining a bubble sucking the lifting surface upward, and the airflow on the bottom pushing the lifting surface upward like a stone skipping on water on the other hand? Gets you good mileage on being able to imagine things.

The vacuum visualization is even more relevant at supersonic speeds, as at that point, your "flight regime" becomes "exotic chemistry occurring is a compressed flow" and an ever increasing column of air getting picked up and carried along with you as you rip a gigantic hole in the atmosphere and carry it along with you; turning aircraft operation into a balancing act between skipping off the atmosphere correctly, and not becoming part of the exotic chemistry you're causing.

Once you get the rudimentsdown though, everything becomes averageable vectors, which makes stuff like KSP with FAR a fun thing to mess with.