You could symbolize the DEM according to elevation for visualisation.
The Identify tool can be used to click on individual pixels within the DEM to return an elevation value. It's the I symbol in a blue circle in the blues tool bar.
Is this what you mean or do you have a points layer you want to extract values to?
This is what I meant, but I think it is better to extract values of elevation to a points layer. But I don't have the points layer yet. How would I make such a layer?
And then, how would I extract elevation values to this layer?