Server Access Log

I am having problems with my site being picked up by search engines such as Google and a few sites have mentioned to check my "server access log". This is a log on the smartftp server which I could have a look at to see if any "robots" or "spiders" have tried to search my site.

Is this a question? And what "SmartFTP server" are you refering to? In fact, this is not related to FTP at all. What people suggested you to do is to look at the web (not FTP) server log your site is running at to see if the Google indexer came to visit your site. You need to login to your site via SSH and take a look at the e.g. Apache access logs.