That shouldn't be a problem.
I would like that the 4 motors run with 5V when the button is not pressed. Then, when pressing on the button, 2 motors began to run faster and two other start to slow down.
The two most important concepts in programming are conditional execution, such as [u]If-Statements[/u] (if-this, do that) and [u]loops[/u] (doing things over-and-over, usually until some condition is met).
First, I suggest you read-through the Programming Language Reference and look at some of the examples so you can get an idea of what you can do and what the programs ('sketches") look like. You won't understand it all or remember it all, but it won't take you that long to read-through the language reference, and it should give you some ideas.
Then, I suggest you get a switch or (push-button switch) and a couple of LEDs (and the required "current limiting" resistors for the LEDs).
You can actually do some things with the pin-13 LED already on the board, such as turning it on & off or dimming it when you push a button.
LED are dimmed using PWM, and DC motors are controlled the same way. So, you can do a lot of relevant experimentation with LEDs before connecting motors. PWM simply means switching on & off rapidly with a variable duty cycle... If the LED is on 10% of the time and switching rapidly, it will appear dim, or the motor will run slow. PWM is built-into the Arduino (as you'll see when you read the language reference).
The trick to project development (especially software) is to take it one step at a time! Add one or two lines of code at a time (or whatever minimum amount of code that makes sense and compiles), and then compile & test that code before moving on. As you gain experience, you can write more than one or two lines at a time, but NOBODY just sits-down and writes a whole program... Programs are "developed" one-step, or one-part at a time.
The Arduino can't directly put-out enough current to power a motor. And, most computer-fans are 12VDC. There are examples of how to "boost" the voltage and/or current with a transistor or MOSFET. PWM will work fine through a transistor or MOSFET
Some (3-wire) computer fans have speed-feedback so you can precisely control the speed. This can be VERY helpful because if you set your PWM fan-speed to "25" (that would be about 10% of the 8-bit maximum of 255) the fan might not get enough power to start moving. With feedback, your software would know to give it more "juice" and then it would start regulating speed. But, speed-feedback makes your software more complicated, so that's something you can add later, if you have 3-wire fans, and if you feel you need it.
I suggest you start with the basic Blink LED example. Then, modify the sketch to make the LED dim... Just try to understand how the output-side of your software can control the brightness of an LED, or the speed of a motor. There are LED dimming examples, but modify the code to do something you want to do!
Next, add a push-button switch. This is the input-side of your hardware & software. Modify your sketch so the switch does something to the LED. Maybe make it dim when you push the button once, then bright when you push it again... Whatever you want to do. Then back to dim when you push the button again it again (remember loops!). The idea is to understand how the to make your sketch do something you want it to do when you push the button.
Now, add a 2nd LED that works the opposite way... One LED dims while the other get's brighter, etc.
Now, that you know how to control the brightness of an LED with software, you know how to control motor speed. It's time to connect the motors and motor-driver circuit. I'd leave the LEDs connected to help with troubleshooting. When the LED is off, the motor should be off. When the LED is dim, the motor should be running slowly, etc. The motors are unlikely to be "linear", so half-brightness may not be half-speed. You can experiment and tweak your code as necessary.
Once you can control motor speed by reading the push-button, you can refine your code and add the finishing touches, etc.