These are the basic steps for cloning a WordPress site. In this example, I assume your source web server is your live site on your web hosting and your target web server is your local development web server. Try to keep the same directory name and database name to keep things simple.

1. Backup all of the files from your site on your web hosting and download (e.g. via FTP).
2. Export your database to a SQL script (e.g. through phpMyAdmin for MySQL)
3. Extract your files to your local development server directory
4. (Create) and import your database using the exported SQL script (e.g. through phpMyAdmin for MySQL)
5. If your database name or database user/password has changed, update wp-config.php in the main directory accordingly.
6. Start your SQL tool (e.g. phpMyAdmin for MySQL). You will need to update the table wp-options. The two options you will be updating (option_name) are siteurl and home. Change these from the URL of your source site (live site) to your local development web server URL (option_value fields).

Hopefully your local development site is now working.