Before you mess around i suggest to read up on terms and issues you might stumble on ! Learn adb/fastboot commands to the bone and then start all the rooting stuff.
Phone on :
Hold power + volume up, when the screen turns black (the reboot) you switch from volume up to volume down and keep the power button pressed all the time in this process. Release the buttons when you entered the bootloader.
Phone on and fastboot enabled :
Open a fastboot terminal on the pc and type :
Adb reboot bootloader
That should get you started.
Thank you so much. I was finally able to fix my HTC M8 with your method advice only. I have been googling a lot of other solutions that worked for other people but they never mentioned to hold the power button the whole time and just switch the volume up button to volume down at the right moment. Hats off to you sir!