How do I get access to the CSS Editor

Without being rude, it will probably cost more to fix what you break instead of asking them in the first place! – however, you can’t learn until you break!.

If I were you and you are interested in trying to play around with CSS/HTML – then you could always install WordPress locally on your Mac/PC, there are plenty of guides around & Videos on youtube.

But to answer part of your question, yes, if they make you an admin in the dashboard area, under ‘Appearance’ there’s an editor button – and that should allow you to change theme files and CSS files without FTP access however: ** BIG WARNING: changing these files without a site backup or FTP access is risky and can result in your blog/site breaking if you do something wrong! **