This instruction can also be used for installing on Windows 10, the differences are mostly cosmetic.

Note. If you are upgrading from version 10.5.0 or later, the installation will automatically remove the old version. If you have a version older than 10.5 installed, please uninstall it manually from the Control Panel before starting the installation.

Download the license file
Note. If you are outside the SLU network you have to establish a VPN connection to be able to access the license and installation files. See more about VPN here: https://pluto.slu.se/gispub/how_to_set_up_vpn

Type (or copy and paste) \\gis.slu.se\gisprog\Esri\Licenses\singleUse\arcgisdesktop into Windows File Explorer (not a web browser) and hit Enter.
Note. If you are using a computer that is not registered in the SLU Active Directory, e.g. your private computer, you have to login once more to access the file. Remember to put "AD\" before your username.

Copy the Single Use license file to your computer.

Access the installation file
Type (or copy and paste) \\gis.slu.se\GisProg\Esri\ArcGIS\ArcGIS1082 into Windows File Explorer and hit Enter.
Double click the ArcGIS_Desktop_1082_180378.exe file.

Extract the files to your local disk.

When all files are extracted, confirm that the “Launch the setup program” check box is selected and click Close.

The installation will start automatically.

Accept the license agreement.

Select Complete unless you have specific reasons.

Choose the installation locations of the application, default works well for most. 

Note. You will not have this option if you are upgrading. In that case the software will be installed into the same directory as the previous version.

Decide if you want to participate in the ESRI User Experience Improvement program and click Install.

The installation can take awhile, but eventually you will be presented with the following window.

Licensing
The ArcGIS Administrator Wizard will start automatically when the installation is completed.
Select the Advanced (ArcInfo) Single Use option and click Authorize Now

Select the Single Use license file you downloaded to your computer.

Authorize using the Internet.

Complete all required fields.

Accept the default and click Next.

Accept the default and click Next.

Accept the default and click Next.

When the authorization is complete you will see this message.

Confirm that your licenses are authorized.

Click OK and you are done!

It is highly recommended to install the DataInteroperability Extension, make sure you install the same version as your ArcGIS Desktop.

Check for updates! 
ESRI is continuously publishing patches and service packs, so be sure you have the most recent updates installed.