Steps to update rooted Galaxy S6

Updating your Samsung smartphone to a stock firmware

Most Samsung smartphones can be flashed with the Odin Tool.
But before you can flash you have to get your devices model number, a compatible firmware, the USB Drivers and Odin.

1. Get your model number: Visit your settings menue - navigate to "About Phone" and see if you can find your model-number. See here for typical model-numbers of a Galaxy S5.


2. Enter your model number on sammobile and download the most up-to-date firmware. If there is one for your region then take that - if there is no update available for your region you can flash other regions aswell. (If you are experiencing problems with connectivity, flash another modem)


3. Make sure you have the Samsung USB Drivers for Windows installed


4. Follow the steps on the download page of your firmware:

Extract (unzip) the firmware file

Download Odin v3.10.7

Extract Odin ZIP file

Open Odin v3.10.7

Reboot Phone in Download Mode (press and hold Home + Power + Volume Down buttons)

Connect phone and wait until you get a blue sign in Odin

Add the firmware file to AP / PDA

Make sure re-partition is NOT ticked

Click the start button, sit back and wait few minutes

This process works for rooted aswell as unrooted samsung phones. Your phone will be running an unrooted (stock) firmware after this process.

To root your phone again - visit Chainfire's site and select the appropriate package for your device-model. Then extract this file and flash it like the other package. (Start Odin, select the .tar.md5 file into the AP/PDA slot of Odin and start)

Use a custom ROM

You can also use a custom ROM to update your phone to a newer android version. You'll need to install a custom recovery (like TWRP) and download an appropriate ROM zip.

Download Odin v3.10.7

Extract Odin ZIP file

Open Odin v3.10.7

Reboot Phone in Download Mode (press and hold Home + Power + Volume Down buttons)

Connect phone and wait until you get a blue sign in Odin

Add the TWRP Image(https://twrp.me/devices/samsunggalaxys6.html)(twrp-3.0.2-0-zeroflte.img.tar) to the AP-Sector of Odin

Make sure re-partition is NOT ticked - disable the Option "Auto-Reboot"

Click the start button, sit back and wait few seconds 

When it is done (Odin shows the "PASS" message) - press and hold the Volume Up+ Power Button on your device until it restarts - release the power button as soon as see the boot-up screen.
If you want to install ROMs - visit XDA-Developers and look into the Android Development section.

If you have downloaded a ROM zip, copy it to your device, boot into TWRP and wipe /system, /cache, /dalvic. Flash your zip file with TWRP and boot up to the new ROM :)

Sources and further reading:
Root Samsung Galaxy S6 and Install TWRP Recovery (All Models)

Warning: This process will very likely trigger the KNOX fuse and you're going to loose warranty in most regions.