1. Interview website owner or webmaster to get a good grasp of the site's purpose and goals.
2. Perform a keyword analysis to find best performing keywords that should be used for that site and for individual pages of the site
3. Analyze site content to determine usage of relavant keywords and phrases. This includes visible text as well at titles, META tags, and "alt" attributes.
4. Examine site navigation
5. Determine the existence of robots.txt and sitemap and examine those for effectivenes.
6. Make recommendations for changes needed for the site and each individual page.

I would update the old site with permanent redirects to to new page for every page. Then I would attempt to remove old content from the major search engines to avoid duplicate content issues.

# 1 issue is visible text being relevant to expected search terms.
# 2 would then be page titles
# 3 is navigation and "alt" attributes for navigation items and link text.
# 4 would be "alt" attributes for images and other media presented on pages.

I discourage the practice for the most part. There are more effective means of paid marketing. One exception would be purchasing listings in highly reputable directories such as Yahoo directory.

Seo is search engine optimization and is the process you use in getting your pages to place well on search results. SEM is search engine marketing and involves purchasing advertising space on search result pages. Sponsored listings are SEM. Both are related though! When using Google Adwords, the better you optimize your pages for search, the less you will be paying for your selected keywords in the PPC campaign and the better placment your ads will get.

I check the competitors backlinks to find hightly relevant sites and request a link from them. If reciprocal linking is required, I may be able to place a lik back to them in a relevant portion of a page on the site but if not, I will state so and may not gain that link. Another method I use is to submit press releases to relevant media.

Social media such as social networking sites and news sites can provide for viral marketing. Viral marketing has proven to be powerful if the content of a site is appealing.

I would avoid any site with the appearance of a link farm. I would also avoid any "spam" practice such as unsolicited email campaigns, certain affiliate advertising sites, sites that re-direct visitors to your site, and anything resembling the practices of Zango.