This is something we might never understand because it is the will of Allah, but I will do my best to give an allegory to try to make it understandable to some extent.
Firstly, I want to make sure that no one is under the impression that this contrast between human free will and qadr is an "accident" or "mistake" by Islam; that it was unintended, and the only reason this problem appeared is because of two unrelated verses in the Quran giving contrary meanings.
In fact, this contrast was intended. Allah mentions the two (free will and Allah's will) together in back to back verses multiple times, so it wasn't as if it is some unintended contradiction. But, rather it was an intended contrast.
Allah says in one instance of these verses:
This is a reminder. Let whoever wills, take the way to his Lord.
But you will only will to do so if God wills- God is all knowing, all wise. (76:29-30)
These verses show the basic belief of Islam about this. A person chooses in his own free will. But the person only wills if Allah wills.
Meaning, Islam's belief is that the two things are compatible.
How exactly are they compatible?
I can only try my best to explain, but the fact is that they are compatible. We believe in it because it was revealed in Allah's book. The question of how does not exactly benefit anyone.
Even if someone cannot understand how it is compatible, he would still want to come to the right path and go to paradise right? Because as most people realize pain is bad and pleasure of Paradise is good. So, he would still work towards that goal regardless of whether he understands whether his working towards it is because of Allah's decision or his own decision.
This is the allegory I will use:
Imagine there is a computer with infinite memory and infinite processing power. There is a program put into it capable of free will regardless of however much memory or processing power that might take. As in, that program chooses for itself with its own decision.
Now, imagine the program is given a choice between:
A) press the button
B) not press the button
The program chooses option A and pressed the button. But, after that, the program starts blaming the computer for its actions saying: "I didn't chose to press it, it is the computer who made the final decision!"
"After all, the computer's processor is the one that actually clicked the button, and actually he executed every line of code inside me. So, it must be his decision."
The question is: who choose to press the button? The computer because it literally computed every line of code in the program? Or the program itself?
The answer is that it was both of them. Computer is the one that controlled the decision literally implementing and calculating it, and the program decided.
The question of free will and qadr is very similar.
Qadr, in fact, comes from the meaning of "calculation" or computation. Allah's qadr is in a way his calculation and computation of everything that will happen.
The universe, as a whole, only moves forward every second because Allah calculates and tells it exactly how to move forward. Otherwise nothing would happen and nothing would exist.
Allah created humans to have free will inside this qadr. They choose what they choose, but He calculates everything. Everything they decided was through his decision, through his qadr, or through his calculation. But, they still decided it with their own will just like the program still chose to press the button.