Google is the search engine giant and many businesses aim to get their website listed in the top three positions on Googles search engine results pages, for their top keywords / phrases. If you are not going to be doing paid for ads then you will need to rely on search engine optimisation techniques to give your site the boost it needs to get to the top.
There are a number of elements to search engine optimisation such as on page meta data, content and URL structure through to external link building. If you really want your site to do well, you should try and do a number of these processes in order to give your site the best chance.
If there is a lot of competition for the phrases that you would like to rank well for then you may need to concentrate your efforts on some more specific phrases that may attract less traffic but will be easier to rank for and should give you a high conversion rate. Be sure to have some way of checking your rankings are improving – you may wish to do this manually but if you have a lot, then you can invest in some automated software that will run the keywords/ phrases for you.