1. Do not purchase a new domain unless you have to.
The search engines put a lot of stock in how long your website and domain have been around. While you can purchase a new domain and redirect your old one to the new one, your best bet is to use your existing domain/website if at all possible. If you're redesigning or starting from scratch and you have to use a brand-new domain for some reason, you can expect at least somewhat of a loss in search engine traffic. It could be anywhere from a few weeks to a few months or more.
2. Optimize your site for your target audience, not for the search engines.
This may sound counter intuitive, but hear me out. The search engines are looking for pages that best fit the keyword phrase someone types into their little search box. If those "someones" are typing in search words that relate to what your site offers, then they are most likely members of your target audience. You need to optimize your site to meet *their* needs. If you don't know who your target audience is, then you need to find out one way or another. Look for studies online that might provide demographic information, and visit other sites, communities, or forums where your target audience might hang out and listen to what they discuss. This information will be crucial to your resulting website design, keyword research, and copy writing.
3. Research your keyword phrases extensively.
The phrases you think your target market might be searching for may very well be incorrect. To find the optimal phrases to optimize for, use research tools such as Keyword Discovery, Wordtracker or Google's Keyword Tool. Compile lists of the most relevant phrases for your site, and choose a few different ones for every page. Never shoot for general keywords such as "travel" or "vacation," as they are rarely (if ever) indicative of what your site is really about.
4. Design and categorize your site architecture and navigation based on your keyword research.
Your research may uncover undiscovered areas of interest or ways of categorizing your products/services that you may wish to add to your site. For instance, let's say your site sells toys. There are numerous ways you could categorize and lay out your site so that people will find the toys they're looking for. Are people looking for toys to fit their child's stage of development? (Look for keyword phrases such as "preschool toys.") Or are they more likely to be seeking specific brands of toys? Most likely, your keyword research will show you that people are looking for toys in many different ways. Your job is to make sure that your site's navigation showcases the various ways of searching. Make sure you have links to specific-brand pages as well as specific age ranges, specific types of toys, etc.
5. Program your site to be "crawler-friendly."