Here are the basics to optimising your own website.
This checklist highlights the areas you need to get right on your website before building any links.
Of course before you even begin your SEO journey you'll going to need to understand exactly what people are searching for so you know what to optimse for. The best way to start is to use one of the free keyword tools to work on. This can be very time consuming but well worth it.
Start off with a "top level" query. So for example, if you have a pet shop type in "pet shop" or even just "pet(s)" to see what's there. Then hone down to phrases that people search for less often.
For a new site it's probably best if you optimise for phrases that get a few searches per day - why? because you'll a) be able to test out your SEO skills and b) less people will be optimising for these phrases so you'll likely have more success.
It's better to be number 1 for 10 phrases that will get you 50 visitors each than for trying for a difficult phrase that may eventually get you 500 per day.
Try the seo book keyword search tool here
If you undertake this research but are still struggling for phrases then a synonym search is also a good idea. Use the Google Adwords Traffic Estimator tool here but be very careful with the numbers that are given. These are "broad match" results which means the volume they provide for (say) "cars" includes every search ever made with the word "cars" in it. It's best just to use this for phrase research then use the seobook tool for the numbers.
You should ensure that the keywords and phrases you are targeting on the page not only appear in the H1 tag but also in your body copy.
Ensure all of your pages point back to your index page. But also ensure you just point it to your root domain. Do not add in the index extension such as index.php or index.html as the search engines will treat this as an additional page and you may find yourself with duplicate content issues.
Also ensure you only have one version of your site either starting with "www" or not. You can permanently redirect your site using .htaccess - look up canonical issues for more information.