Acquiring some inbound links from other websites will help get your site indexed quickly. As for ranking, that depends on how competitive your key phrases are, but again inbound links will help.
If the site is brand new, I wouldn't discourage yourself by checking your rankings in Google. It's going to take a while to rank well in that particular engine.
If you want some initial encouragement, I recommend checking MSN / Live search. You'll see your site begin to rank there long before Google.
Hope that helps.