Hi Alex, You would setup wordpress locally much like you set it up on the server.
Here are the steps I usually take. I'm assuming you have MAMP setup and running properly.
Database - Start MAMP and go to phpMyAdmin. Create a new database for the site. Name it whatever you want.
Install WordPress - Create a folder in your local root directory for the site. Drag a fresh copy of WordPress into that folder. If you don't know where the root directory folder is, open the MAMP control window and click Preferences > Apache and select the root folder you want to work in.
WP-Config.php - Rename the config sample file and point WordPress to your new database by updating these three lines.
/** MySQL database username */
/** MySQL database password */
Copy the Database - Export your current database in .sql format (no compression) and import that file into your new database.
Update wp-options - Go into the database locally and update the url in the wp-options table. Should be option id 1 & 37. The url should be something like http://localhost:8888/foldername.
wp-content - Next you need to get the live wp-content folder. The uploads folder could be huge so if you are just doing some theme edits you might be able to get away with not downloading that directory. Otherwise download the folder and copy it into your local instillation.
Find and Replace - Now you should be able to login to the site locally. The last thing I do is run find and replace on the whole site to update all the urls from whatever the domain name is to the local url. That way all your paths will work locally. You will need to redo this when you upload.