To figure out your DPS in ESO you can do a few things. On both PC and Console the Target Dummies in your own house show your average DPS after you completed your test in the chat window.

However, on PC you also have the option to download addons like Combat Metrics which show the average single target and area of effect damage during the fight. In addition, the addon also lets you analyze your fight afterwards in great detail like you can see in the image below.

Stamnecro 100k dps parse ptsweek1