what is the best way to connect an additional display to an imac desktop

What year model iMac?

see > Identify your iMac model - Apple Support

To connect a display to a 2017 or later Thunderbolt 3/USB-C iMac model,

see > Connect an external display to your iMac - Apple Support

To connect a display to a 2015 or earlier Thunderbolt 2 iMac model, requires using a Mini DisplayPort adapter.

Depends on the model of iMac, but generally using one of the Thunderbolt ports provides the best results and highest quality image.