Coding a Stirrer with Different Speeds
The above comments are spot on.  It sounds to me like you are new to the Arduino, so the very first thing to do is go to the Arduino Reference page https://www.arduino.cc/reference/en/.  That shows you the basic tools you will need to work with.  It's not obvious from that page, but analogWrite() is what you use for the PWM, as explained if you click on that topic.  Note that it only works on certain pins.  Don't worry about controlling a motor at first, just control the brightness of an LED until everything is debugged.
You mention 3 different intervals.  Are each of these to give equal on and off times, and just keep repeating until you turn the stirrer off?  Or will you have a separate fixed run time and the buttons selects one of 3 different off times per cycle?  Or is there only one cycle, and the buttons just select how long it will be before automatically shutting off?  The answer will determine how you set up the timing.  Assuming that the UNO doesn't need to do anything other than control the stirrer, you can probably do all timing with the delay() function.
You can start with the famous &quot;blink&quot; code.  Once you get that working, change it to use one of the pins that supports PWM (not the built-in LED on pin 13).  The code has separate delay() values for on and off times, which you can set for one of your 3 intervals.  Then change the digitalWrite() commands to analogWrite(), of course with the proper parameters. Now you have the basic system, and can work on the switching logic.