If you only have access to your site thru FPT and not a development environment, then you must program the web pages in the FTP edit environment. You will need to edit each page for the basic On'Page SEO Elements. There are to many to outline here but if you go to http://www.catanich.com/search-engine-optimization.asp this will give you an idea of what you need to do. As for "live FTP editing", first copy the existing site to your local PC and make a second backup of it. Then, one page at a time, do your On-Page element editing. Then upload it back to your server.
FTP is used to upload the files, not to optimize the web pages of your site. To do optimization, you need to understand important methods like directories submissions, social bookmarking, article writing and submission etc to popularize the site.
Here are some things to google: html basics keyword density validation link building strategies. Hope this helps.