I'll divide this in part to answer you question better.
1. Search engine optimization
Works by slowly bringing your website to the top of the search engines. I really suggest you read this. It solved all the doubts I had as a newbie:
http://en.wikipedia.org/wiki/Search_engine_optimization
2. Paying for it
You can pay a company to do
SEO for you. If you do it yourself it's free... but hard work.
3. Paying Google
Google can't be bribed for
SEO. You can bribe them with AdWords

It's their alternative to
SEO that gets you to the top of the listings.
4. Long Term
No, it won't stay there forever. You need to work on keeping the ranking there. Plus, competition and algorithm (the Google algorithm that defines who's at the top of the SE) changes can affect your position.