SEO Your Website

Before you write one line of code:
Do keyword research to determine what keywords you want to target
While constructing your website you should do the following:
Use markup to indicate the content of your site
Optimize your tags on each page to contain 1 - 3 keywords
Create unique Meta Tags for each page
Use header tags appropriately
Use tags if appropriate
Optimize your URLs
Use Search Engine Friendly URLs (for dynamic sites)
Use keywords in your domain (http://www.keyword1.com/)
Use keywords in your URL (http://www.example.com/keyword2/keyword3.html)
Use dashes instead of underscores to separate words in your URLs (keyword2-keyword3.html)
Optimize your content
Use keywords liberally yet appropriately throughout each page
Have unique content
Have quality content
Use search engine friendly design
Create a human sitemap
Do not use inaccessible site navigation (JavaScript menus)
Minimized outbound links
Kept your pages under 100K in size
Design the navigational structure of the site to channel PR to main pages (especially the homepage)
Create a page that encourages webmasters to link to your site
Provide them the relevant HTML to create their link to you
Provide them with any images you may want them to use (although text links are better)
Make sure your website is complete before launching it

Immediately after launching your site you should do the following:
Submit your site to all major search engines
Google (Use a Google SiteMap)
Yahoo (Use the page list option)
MSN (Finds your site via incomming links)
Ask (Finds your site via incomming links)
Submit your site to all free directories
DMOZ (also powers Google Directory)
JoeAnt
Submit your site to relevant directories
Find more at ISEDB
Begin a link building campaign (attempting to get keywords in the link anchor text)
Put a link to your website in your forum signatures
Reply to relevant blog posts (Don't spam please)
Submit articles to relevant websites

If you will pay to promote your website:

Submit your site to pay directories
Yahoo
GoGuides
Purchase text links from high PR (Pagerank) sites related to your site
Finally, as part of an ongoing strategy:
Continually update your website will quality, unique content
Continually seek free links preferably from sites in your genre

Do NOT do the following:

Make an all Flash website
Use JavaScript for navigation
Spam other websites for incomming links
Launch your site before it is done
Use duplicate content
Point several domains to one site without using a 301 redirect
Use markup inappropiately
Style eader tags to look like regular text
Hide content using 'display: hidden'
Use other "black hat" techniques (unless you accept the risk - Banning)
Doorway/Landing pages
Cloaking
Hidden text
Keyword stuffing

Additional Tips:

Usable and accessible sites tend to be search engine friendly by their very nature
Be patient! High rankings don't happen overnight
Don't obsess with any one search engine. They are all worth your attention.