Root file

The precise steps you need have much more to do with which hosting service you are using than which computer you use.
As I understand what you have said:
You have Filezilla running ?
Your filezilla is configured to access your web hosting ?
You have downloaded and expanded the wordpress files onto your MAC ?

If this is the case then:
Run filezilla, login/connect with your web hosting. So now you have a split screen file manager view.

On the left hand side browse to where you have the wordpress files unzipped. Upper left will have the folder, lower left panel will have folders named “wp-admin, wp-include, wp-content”, and quite a few files.

On the right hand side is your web hosting files. You may need to expand folders. The file name you will put your website files in depends upon which software your hosting company is using. It may be “public_html”, possibly it is “htdocs”, if you can’t work it out contact your hosting company support. So lets say it is public_html, you would click on it in upper right panel, lower right panel will then show its present contents, possibly empty.

To upload your wordpress files you would click the first folder in the lower left panel, then shift+click the last file in the list, then select UPLOAD. A thousand or so files will be queued to upload.

Create your customised wp-config.php from the sample file, and upload it and otherwise complete the install process described here: http://codex.wordpress.org/Installing_WordPress