i suggest you start by reading this
you are not changing your URL but many of the steps outlined on that page are ones you need to do to move your data over.
you have to create a new database - the "new" install is OK as it will create a database and a new wp-config.php file (which tells WP where to find your database and how to log into it).
after you've made the new database, back it up. Because you are going to overwrite it with the data from your old database backup file.
You won't have to change any URL's in your restored data (that is referred to in the page I suggest you read) because you are using the same URL you had before. But the procedure to import is the same.
If you get stuck your webhost should be able to help you.