Well, to me the mark of a great actor is a great imagination. I agree with Zultana, that you should begin with a piece that speaks to you. As you get used to portraying anger or sadness on cue you'll be able to imagine the feelings that your character will have in any given situation.
I'm actually quite good at dramatic pieces and struggle a little with comedy. When I would get upset as a child I used to cry to my reflection, which is probably why facial expressions are easier for me to portray in dramatic roles. Try being sad in front of the mirror for a while. This does not work for everyone because they think they look ridiculous and end up laughing, but it works for me or I would not suggest it. I don't know if your drama instructor has taught you this, but there are five basic facial expressions that can be combined to portray any emotion; happiness, sadness, anger, fright, and surprise. Practice each of these in the mirror as well.
My final suggestion is, do not be afraid to get loud. Dramatic scenes are best when at the height of emotion the soul of the character cries out in utter frustration, anguish or despair as per the situation.
Hope this helps. Break a leg!