There are some awesome resources online to help you with this process. Good for you for setting up a local development environment. I think you will find it to be an awesome change to your workflow, but be prepared for some trial and error in getting it right.
First of all, there is an excellent article on the Codex for setting up WordPress on MAMP: http://codex.wordpress.org/Installing_WordPress_Locally_on_Your_Mac_With_MAMP. This article on Smashing Magazine also does an extraordinary job with the topic: http://wp.smashingmagazine.com/2011/09/28/developing-wordpress-locally-with-mamp/.
Next, to export your database, the Codex also has a great article (note that backup/export as essentially synonymous in this case): http://codex.wordpress.org/Backing_Up_Your_Database#Backup_Process_with_phpMyAdmin.
I would also recommend if you will be messing with the database to get Sequel Pro, a free database management application: http://www.sequelpro.com/. To import your database locally, see item 2.1 on this page: http://www.sequelpro.com/docs/Frequently_Asked_Questions.
I’m pointing you to external documents because your question would warrant a HUGE response here that I think is covered well in bits and pieces online. Feel free to ask follow-up questions. There is a lot of trial and error in getting this right, so I recommend preparing to do a lot of reading and having patience in the process. Your effort will be worth it in the end!
Good luck!