For most users on Steam, the update process is handled automatically by the client. Launch Steam and go to your Euro Truck Simulator 2 in your list of games.
: Version 1.36 may break many older mods. If you rely on specific mods, check the SCS Modding Wiki for compatibility. How to Install the Update For Steam Users
Ensure at least 5-10 GB of free space on your drive for the installation files and potential mod unpacking.
Dual-core CPU 2.4 GHz (Quad-core 3.0 GHz recommended). Memory: 4 GB RAM (8 GB recommended).
With DirectX 11 efficiency, you can safely bump your scaling up to 300% or 400% on mid-range graphics cards for crisp, aliasing-free text and power lines.
Summary
Go to the tab and ensure it is set to "Always keep this game updated".
Assuming you are on the Steam branch (the only civilized way to play), the process is deceptively simple. But "simple" hides the carnage.
: This is the "long feature" of this update. Version 1.36 fully transitioned the game to DirectX 11 and completely removed DirectX 9 support
In the same properties menu, go to Local Files and click "Verify integrity of game files" to ensure no corrupted files are downloaded. How to Update ETS2 (Non-Steam/Retail Method)
If you load a 1.35 save game into 1.36: