How to Create a Local Copy of a Live WordPress Site

This process is quite involved but definitely doable. A search on moving a live site to a local server will probably be able to provide more detail but I'll summarize the process below.

1. Make a copy of your live database. This will be an .sql file which you can get by exporting your database in phpmyadmin on your live site.
2. Make a copy of all your wordpress files and folders on live site. Can be accomplished by downloading your files through ftp.
3. Setup your local development using MAMP, WAMP, etc.
4. Copy/Paste wordpress files and folders into your local server folder
5. On your local development site create a database and import your live database (.sql file) .
6. Update your server information (db name, db username, db password, etc) on your wp-config.php with the info used when making your local database.
7. Although your database is populated the url's are still pointing to your live site and will have to be updated I personally use a search and replace script like interconnectit's Database Search and Replace Script in PHP.

There are plugins to help with backing up your live site but I can't personally vouch for any.