Now that I have told you about how I began writing calligraphy, I will help you get started. Before you go out and purchase any books, pens, or paper, get a pencil, and search on google: Calligraphy Alphabet. You will get to choose from many different alphabets. I suggest choosing foundational hand calligraphy, as it is extremely easy to pick up on.
Look at your computer screen, and try to replicate the letters that you find. Most likely, you'll have a hard time. First, you must remember that you are writing in a pencil, not a broad tip pen, therefore you will have different results. If your letters look just like the skeleton of the ones on the screen, you may be ready to buy a calligraphy book. (They will give you samples to copy from)
If not, practice your handwriting. Any time that you are writing something, try to write neatly. As you do this, you'll see yourself developing neater handwriting, and you'll be ready to buy that real calligraphy pen.