Crema

Crema refers to the natural froth that fills the top of the cup without milk or additional ingredients. Done well, this can cause the coffee to appear as if milk has been added. This can happen on accident but many brewers will go out of their way to get a layer of crema.

I like the crema because it's both visually pleasant and provides a nice mouth feel for those first few sips.

Silt

After drinking, pay attention to what remains in the cup. Ideally, the look and consistency at the bottom of the cup should be the same as the rest of the pour. If a dark silty layer appears at the bottom, you may want to change your filter. This can often result when using a permanent metal filter which allows larger solids to pass through than would a paper filter.

Reheating

If your coffee goes cold, the only good way to heat it back up is to add more of it from the insulated pot. Anything else will increase the temperature to the great detriment of the taste of the coffee.

Cupping

Cupping is the de facto way to taste coffee and is often in practice with roasters when fine-tuning their roasting parameters.

The process of cupping usually involves a special wide-bowled spoon. This spoon is filled with the freshly roasted coffee and slurped in the rudest, loudest way you can imagine. This slurping oxidizes the coffee giving it a bright but fleeting boost of its volatile flavors.

Temperature

If you find the need to wait for your coffee to cool down before drinking, you may be making it wrong. The following is slightly opinionated on my part and everyone is different but I'll give you my reasoning.

Coffee shouldn't be made with boiling water. Brewing water should be no hotter than about 98-98.6 degrees C. This is still pretty hot, but stepping off from 100 degrees C boiling at the start of the brewing process means the end result should be that much colder. Adding to this, proper brewing methods should also be somewhat slow for non-espresso drinks. This shouldn't make for a cold cup per se, but I'd expect the final product to come in at optimal drinking temperature right after brewing.