Being listed in Google's search engine is free. They have indicated
that, unlike other search engines, they will never charge a fee to be
included in their index.
The correct place to submit your website is:
Google has created a page of information regarding being listed on Google:
Submit your URL
It is important to realise that after submitting your site it can take
a month or two to show up in search results.
The most important thing you can do is to get other sites to link to
yours. If no other site links to yours, Google may choose ignore it
(rare, but happens). You should also submit your site to the most
appropriate category at Open Directory:
It is probably worth your while to read the entire Google Info for Webmasters:
If you require any advice specific to your site, just post the URL in
a request for clarification and I'll get back to you.
All the best,