The search engines you are hoping to rank well on can be one of your most helpful tools in finding new places to submit your site. Simply search for your keywords plus the phrases "add url" "add site" "submit url" "submit site" "add link" "submit link" "suggest url" "suggest site" or "suggest link". And you should be presented with a list of locations that accept submissions related to your topic. These can be niche directories, or merely link pages on content sites. Some places may have automated link submission forms you merely need to fill out, others will provide an email address. So long as the submissions are free and do not require a link back you should make a submission.
Another thing you can do as well is search for the backlinks of your competitors. The standard syntax of this is typing "link:http://www.example.com" into a search engine. You should do this search on multiple search engines so you get a more varied and complete data set. This practice is generally referred to as link research.
Browse through the links once you find them and look for ones that would take submissions. Even if it isn't evident that submissions are welcome consider dropping a friendly note to the webmaster of the site (but only if they solicit comments, don't just pull an email address off of WHOIS information and assume it is okay to email them) and ask them to consider adding your site. Be honest and forthright and don't promise anything in return. You may get a link, you may not, but you'd be surprised how often you can get a link in this way without having to link back or pay.
For any of the above submission methods you need to realize that it is vitally important that your website be complete, and with high quality original content. Yes, you can easily get free links from the places I've mentioned, but not if your website is generic-viagra-for-less-and-mortgage-loans.com. Do not try these submission methods if you're making a poor quality short-term site to spam with, it will not work and not be worth your time. These methods are only applicable for quality content sites that won't immediately be turned away because of their low quality content.
Viral marketing is the creation of content so compelling that every visitor who sees it refers at least 2 more people to it, thus creating a traffic pattern that mimics the spread of a virus.
Social media & bookmarking sites such as Digg, Reddit, Del.icio.us, and others have changed the way viral marketing is often done by providing a built in audience to the viral marketer so that all the viral marketer needs to do is get his page on these sites.
At the most basic level social media optimization would be the use of buttons, such as on this site, to allow visitors to easily "bookmark" your site using one of these services. This is passive optimization and can result in big traffic if an article catches on, but more often than not it doesn't.
A more active method of optimization would be purposefully crafting an article to appeal to the audience of one of these sites. For instance Digg has a largely male, largely young, and largely technophile audience, they also like short, to the point, interesting articles. Already people have, in jest mostly, published formulas for getting a page well received on a site such as Digg based on the types of articles that normally do well there and the demographic. So the typical Digg article is a top 10 or other such list of interesting & somewhat nerdy facts. Perhaps the top 10 ways to trick out your PC, or the 5 most promiscuous comic book heroines.
This is fine if your site is about PC tweaking or comic books, or any other topic you could massage to fit the Digg audience, however often people will make content completely unrelated to their site in hopes to gain link weight through social media popularity. This would be considered by most to be spam and the people who heavily use social media sites are growing hip to it and so you run the same risk as you do when doing scandalous link baiting, namely a big backfire that blows up in your face.
Another way to do viral marketing through social media is to commission a funny video be made and submit it to YouTube or another video sharing site and either through product placement or a byline at the end reference your website or product. Large billion dollar corporations do this method now, but the beauty of it is that unlike a Superbowl ad you do not need millions of dollars to do this, you just need a cheap camcorder and an idea. However, people prefer authentic content and not content made to promote a business, so this as well can backfire. However, perhaps due to the public's desensitization to advertisements in video (see TV) this type of activity is seemingly not frowned upon as much as the social bookmarking manipulation mentioned above.
Regardless of what you do, the purpose of viral marketing or social media optimization is not to gain links directly from a social media site, but to build buzz and or interest in your site among bloggers and other content creators so you can gain thousands of new incoming links from a wide variety of sources.