You can achieved black and white with your camera just fine. You could either changed the mode to black and white, or changed the color later in your computer into black and white. Fluke is fine, as long as you learn from it - what you did right and what you did wrong. Writing down notes on how you took the picture, when, and all the info that you think is useful write it down - unless, you have good memories and able to remember what you did. Sometimes I have to write it down myself, but since I have a bit of a good memory and experiences, I seldom do, but I do remember what I did.
Without samples of what you have done, can't really comment on how you can improve or what went correctly. Since you have a DSLR, you can go on a shooting assignments. When taking pictures you need to developed skill so that you can mentally see things in tones of black and white and gray. Most photographers have that skills, as well as able to see composition in their head.
Composition, composition, composition... without it, images just suck. If you can get a hold on photography books (libraries should have them), try to get them. You can learn by looking at good examples.
Your assignment - shoot around where ever you can - look for light and shadows. Here are some good examples of it:
Feet and Chair, Teresa #2, #3, Julia with guitar
http://www.paulpolitis.com/bwgallery/people/
Shadows and light: (A good example of ABSTRACT - "Kitchen Sink")
http://www.paulpolitis.com/bwgallery/objects/
Playground at Night, Regal
http://www.paulpolitis.com/bwgallery/night/
Abstraction
http://www.paulpolitis.com/bwgallery/nudes/
[ADDITION:
http://www.paulpolitis.com/bwgallery/objects/default.asp?p=2&f1=&f2=
"Longing" is NOT a good example of light and shadows, just want to clarify that not all things with shadows is in reference to the "light and shadows" I'm talking about. "Windowsill" is a GOOD example, though. ]
Look at those images and see why they are working. You have compositions, light and shadows, a bit of abstracts. With those in mind, go take a lot of pictures and think of those 3 things and a lot of with the abstract. With abstract, you are looking for shapes, lines, shadows and light...
Composition - think of not including unnecessary background, think of not just putting everything in the middle (more interesting if they are not so balance), more details by getting really close can be interesting.
It's digital, so, it's wouldn't cost you to take a lot of pictures. Then you can edit it in your computer. But you want to barely change the picture where it becomes not the real picture. Make notes till you don't need to anymore. Look at the actual image and how it appears in black and white.
After you learned those techniques, you could start learning about shutter speeds, ISO, aperture, and among other things. One step at a time, and soon you'll learn all you want.