It came to me when I was watching the new dev video, I assume when you use an ability with a DoT mechanism it may, say light them on fire or encase them in electrical currents. How are we meant to know when our DoT effect has worn; aside from counting. How will other players DoT's affect what I see?

Looks to be mostly based on visual cues at the moment.

Probably visual, an target who is on fire tend to take fire damage.

You will also see if other players added the effect, not sure if they stack, if two players set you on fire it might give double dot or not