Job Definition
A Search Engine Optimiser (SEO) differs from a Webmaster and a Web Designer in that he or she is responsible for marketing a website, as oppose to designing it.
Basically, a Search Engine Optimiser's knowledge base lies in knowing how Search Engines and Directories index and rank websites and can therefore re-design existing sites in order to raise the amount of visitors they receive.
A basic technical and design knowledge is required for this job, almost to the extent of a Web Designer, but a SEO also needs sound business and marketing skills.
The main factor a SEO has to deal with is the fact that the industry changes on a daily basis, so you have to be able to adapt quickly. It's not what you know - it's how well you adapt to the changes!
Qualifications
Similar to that of a Webmaster but with a less technical focus.
You could learn online what you need to know about Search Engine Optimisation, but an IT or Marketing background would be beneficial to you.
You don't really need any qualifications to be a SEO, but some Web Design knowledge and experience will be necessary if you want to this professionally.
Experience
You will need experience in the following areas to become a SEO:
Web Design
General IT skills
Key Skills
Some knowledge of the following would be necessary:
Search Engines
Web Design
Marketing
Reciprocal Links
Directory sites
HTML
Graphic Design
Keywords
Copywriting
Useful Resources
HTML Goodies - HTML tutorial site
WC3 - World Wide Web resources and standards
Open Directory Project - Largest directory of resources on the Web
Webmonkey - IT tutorials
Microsoft FrontPage - Homepage for MS's HTML text editor
Macromedia Dreamweaver - Homepage for Macromedia's HTML text editor
w3schools - Tutorial site for web design technologies.
WebmasterWorld.com - discussion forum for SEOs
Zero Strategy Marketing News - news and discussions for marketing professionals.
Fused Nation Blog - SEO and marketing blog.