I hope you can learn from my amateur attempt at hand lettering. I'm not sure if it is technically calligraphy, but once you have the finished product, what does it matter?
Here are the markers that fancy people use.
But really, you can use any thin-tipped marker, like this one. Or a pen or pencil.
I hope your cursive isn't too rusty!
Step 1: Write a word in cursive.
Be sure to space out the letters enough.
Pay attention to the movement of your marker - when you move upward and downward. These arrows are just for demonstration.
Step 2: Next to the downward-moving part of each letter, draw a curved line.
The line should run parallel to the letter and usually should touch the letter at its top and bottom. This is to add emphasis.
Step 3: Fill in the areas inside the curved lines.
Step 4) Practice a lot. And get creative!
The most important lesson I learned is to work with your natural style. My cursive letters are thin and tall, but others' are thick. I used to try to mimic other styles, but now I believe that each different take on hand lettering is beautiful and valuable.