Apple - Backup files from Terminal in Recovery Mode

My goal was to copy files to the external hard drive. They are stored in Macintosh HD (I originally thought I will find Macintosh HD in a subfolder of OS X Base System - wrong assumption). There was no Macintosh HD in Volumes folder, because I first needed to unlock it (I use FileVault).

First you need to find the lvUUID of your Macintosh HD. Use this command:

diskutil list // lvUUID

Look for text looking similar to this:

Logical Volume on disk0s2 
4B2EFAAE-C871-4E6D-AB15-2DDE604B97CE // this is lvUUID
Unlocked Encrypted

To unlock use this command:

diskutil cs unlockVolume lvUUID #replace lvUUID by the one shown in the diskutil listing

You will be prompted with password for your user account. After that Macintosh HD will be present in /Volumes/ folder.

All thanks to klanomath for enlightening me. See full Q&A here: No Macintosh HD in Volumes folder

For new macs using disks with APFS (Apple file system) you can simply do:

diskutil apfs unlock "Macintosh HD"

And then access it by:

ls "/Volumes/Macintosh HD"

When booted to OS X Recovery the root of the Macintosh HD is not /, it's:
/Volumes/Macintosh HD/

To get to your Home directory in Terminal, use:

cd "/Volumes/Macintosh HD/Users/User_Name"

Where User_Name is the name of your User Account.

From there you can access your directories such as Documents, Desktop, Pictures, etc.

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When booting into the Recovery Partition, the Macintosh HD does get mounted automatically and should be listed in /Volumes. If this is not the case, run Disk Utility (accessible through one of the menus in Recovery Mode) first to check the drive for errors and have them fixed.