Mac OS X is not starting anymore I tried to install Mac OS X El Capitan and it failed in ~70% progress after reboot and now I even can't start recovery mode (pressing Cmd+R just tries to continue installation process and fails again and again).

Assuming I can get a backup of my user files over Target Disk Mode and then hand migrate them, what steps do I need to perform to wipe and reinstall Yosemite on my Mac?
If you have another Mac, you should make a bootable Yosemite drive. To do that, you need an 8GB USB drive and the Yosemite installer downloaded. Here are the instructions, copied from the linked article:


  
  Connect to your Mac a properly formatted 8GB (or larger) drive, and rename the drive Untitled. (The Terminal command used here assumes
  the drive is named Untitled.) Also, make sure the Yosemite installer,
  called Install OS X Yosemite.app, is in its default location in your
  main Applications folder (/Applications). This means that if you moved
  it before installing Yosemite, you need to move it back before making
  your installer disk.
  Select the text of this Terminal command and copy it: sudo /Applications/Install\ OS\ X\
  Yosemite.app/Contents/Resources/createinstallmedia --volume
  /Volumes/Untitled --applicationpath /Applications/Install\ OS\ X\
  Yosemite.app --nointeraction
  Launch Terminal (in /Applications/Utilities).
  Warning: This step will erase the destination drive or partition, so make sure that it doesn’t contain any valuable data.
  
  
  Paste the copied command into Terminal and press Return.
  
  
  Type your admin-level account password when prompted, and then press Return.
  


When that's done, plug that USB drive into the El Capitan Mac, hold down Option and turn the Mac on, and select Install OS X Yosemite from the list of startup drives. That should bring you into something that's identical to the Recovery HD for all intents and purposes (the only difference being that you don't need to redownload the OS X installer; it's stored locally). From there you should be able to wipe the hard drive and reinstall Yosemite. Good luck!