There are three types of search engine optimization one can perform on their site. You do not always need to do all three, but you do also do not need to limit yourself to just one type. However, the different types can hinder one another so it is important that you pick a main type to focus on the most.
The three types of search engine optimization are:
The steps you must take to optimize a homepage are different from the steps you must take to optimize a content or product page. Additionally the goal of someone optimizing a content or product page is usually different from the goal of someone optimizing a homepage. Your site's topic and the competition may influence your decision to focus on one type of optimization or another. What follows will be an explanation of the three types and a description of the situations in which they are best used.
Homepage optimization is obviously the optimization of a site's home or index page. Sites only have one such page, which is an important factor when deciding to engage in this type of optimization. You see a homepage gives you a single chance to hit your target. You can at most focus on a single major keyphrase and a handful of minor ones. So, for homepage optimization to be your focus, you need to have a major keyphrase that is worth it.
First your keyword research and figure out how often this phrase is searched for. Is the word popular enough? Next check out the competition, do you have any chance at competing with them? For instance if your site is about something general such as "sports" or "books" you probably should forget about optimizing your homepage for such general keywords, the competition is too strong and your energy is better spent on the other two types of optimization. On this site I do not engage in any homepage optimization because words like "web development" are too competitive and "website publishing" or its derivatives are not popular enough.
Assuming your keyphrase is popular and the competition is not insurmountable you can procede to optimize your homepage. The most important thing when optimizing a homepage is to name your site using your keywords. It isn't enough to put your keywords in your title tag, though that certainly is very important too. The actual name of your site, the name appearing in your graphical header or logo, needs to include delimited keywords. By delimited keywords I mean spaces between the words so that someone making a link to your site does not think they're supposed to be run together. For example do not use a run-on domain like "PurpleWidgets.com" as your site's name. If your domain is "PurpleWidgets.com" then name your site "Purple Widgets." It may seem like a minor thing, but it makes a mountain of difference. People will most often link to you using your site name as the anchor text and the anchor text of your incoming links is vitally important to ranking well. It is possible to rank well on keywords without doing this, but you will have to work much much harder and it may take a couple years or more to build up the necessary popularity.
A keyword rich domain can also help, but it isn't required so long as the title and site name are keyword rich. Also you'll want to engage in standard on-page optimization by placing keywords in your body content, headers, and elsewhere.
It is also important that you link back to your homepage from every page on your site, preferably using your keywords instead of just the word "home" or if you like something such as "Purple Widgets Home." This will help send PageRank to your homepage and keep with the good anchor text.