In an attempt to be as clear on the subject as possible here's what you can expect broken down into three (hopefully) easily digested points:
1) You won't hit the top of Google straight away (it doesn't matter what keywords you've used).
Google needs to send its crawlers to your site before your site can even be considered for indexing in the search results.
As a webmaster or SEO professional you can submit an XML sitemap to Google to ensure it knows how many pages your site has - but it won't necessarily speed up the process of becoming indexed. This process can take up to 6 weeks.
2) Once Google has visited your site there are several things that can happen.
a) You may get on the first page of the search results
b) You may end up on the 4/5/6th etc page
c) Your web pages, initially at least, won't be found anywhere in the search results
Why is this? Well it's all down to how well optimised your web pages are for your targeted keyword and how competitive that keyword is (there are other factors but these are the two most important at this stage).
For example if you are targeting the keyword 'tennis equipment' you may not rank initially or your page may be found on the lower pages - which no one will ever see. However, if you've added geographic search terms to your optimised page you may find that search queries with your keyword + your geographic location rank much quicker. For example, 'tennis equipment in Covent Garden' may go straight to Google's first page.
The distinction here is that the more generic 'tennis equipment' will be much more competitive than 'tennis equipment Covent Garden' and hence the difference in results.
3) For those more generic terms it is a question of patience and perseverance. Google will not favour, initially at least, a domain (especially if it's brand new) over an established competitor - even if you think their website is awful. This is because Google takes two things into account when choosing which websites to place on its first page; authority and relevance.
Relevance is (generally speaking) concerned with how well the content on a particular page will meet the needs and requirements of the user who is looking for something.
However it's authority which we're more concerned with here. Domain age and in-bound links are two of the more important factors here and if you have a new website/new web page it will take time to convince Google that your webpage is worth ranking above others that are already established and linked to.
Again, this takes time. It might take 3 months it could take 3 years. It depends on the levels of competition and the strength of that competition. This is one of the reason why in-depth research is needed before selecting the keywords your website/web pages will use.