Choose a style of writing that you would like to emulate. If you want to learn clear cursive writing, calligraphy or other ornamental penmanship, you can usually find online materials.
Look up that style of penmanship in an Internet search engine coupled with the word "Lessons."
Click on a website that appears to have the lessons you want. A site like Zanerian.com has lessons scanned from various magazines like Business Educator. You can then either print out these pages or set the computer up in such a way that you can view the lesson in your browser while practicing your script.
Look for a site that has video of the various script examples, so that you can see how they are formed.
Practice your penmanship skills each day until you are comfortable writing in your new style.