When you taste, smell first, then swirl the coffee to cover all your tongue and palate, then chew a while to get the aftertaste. That way the flavors are easier to discern.
The most standard listing of flavors is on Ted Lingle's
coffee flavor wheel.
The left side of the wheel is not very accurate. First off, it does not show Lingle's intent of classifying the more detailed flavors as combinations of the fewer basic flavors. Second, the idea that flavors can be built up as combinations of four or five basic tastes is most likely false, since there are roughly thirty or so known tongue receptors for specific bitter and savory compounds, with more to come.
The right side of the wheel is very useful. It works by classifiying flavors from the lightest and most volatile compounds to the heaviest and least volatile. An actual coffee' flavors will often be like a slice of pie from that circle, with lighter roasts at the top and darker roasts moving clockwise.
You can start by discerning the broadest categories -- acids (aka "enzymatics"), caramels and distillates -- and then working your way to the more detailed flavors. Here too, I think a revision may be needed. What is classified as nut-like and malt-like needs its own separate division, since these flavors develop earlier in the roast than caramels, and are frequently accompanied by woody, toasty and savory flavors.