I. Whatever is changing is being changed by something else
When something changes, such as when liquid water turns into ice, something else must be applied to it in order to change it. In this case, warm air must change to cold air in order to change the liquid water to solid ice. But the same thing applies to the air as well, because it changed from warm to cold. So something else changed the warm air to cold air. And if that thing changed as well, then something else changed it. And so on in a chain of concurrent causes.
II. The chain of changers cannot be infinitely long
Note here that the argument is talking about a presently existing chain, not a chain stretching back into the past. It is only concerned with what needs to be in place right now to make the change occur.
For example, to make the liquid water change into ice, the freezer needs to be in place, the electricity to run the freezer, the power plant to run the electricity, the atomic structure of the nuclear fuel rods to run the power plant, etc. This chain of concurrent causes cannot be infinitely long because each one is only being changed by its neighbor, and so the chain must terminate in something that is driving the whole chain.
As a sort of "intuition pump" to capture the reasoning here, imagine a chain of roller skaters each with their hands on the shoulders of the one in front of them, each told to just let the person behind them push them forward. If the chain were infinitely long, then they would all be passive pushers and the chain wouldn't move. If it's moving, then there must be a single roller skater at the back of the line that is pushing the whole chain forward.
III. The chain must terminate in an unchangeable changer that drives the whole chain
So at the other end of the chain of changers (e.g. deep in the power plant), the chain must terminate in something that is driving the whole chain.
IV. An unchangeable thing: God?
Something that is unchangeable would not be made out of energy or matter, since both those things can change location, direction, strength, etc. So it would be non-physical. It would also be spaceless and timeless, since being located in space or in time means being changeable (e.g., "earlier" changes to "later"). Being non-physical, spaceless, and timeless means all of them are the same one agent, since there is no way to distinguish them from each other. Being the source of all change and hence anything that occurs or could occur, it is omnipotent. Being unchangeable, it doesn't lack anything or have any flaws and is hence perfect. And being the bottom foundation of anything that every happens or ever exists, it is the "substrate" of every true proposition and is hence omniscient.
For a more in-depth look, please see the full argument.