Doesn't sound like you want to improve your website, just drive traffic. Basically you've got 3 major ways to drive traffic:
search - paid or organic
links - from anywhere, anyone
type in - people going to your site directly, often connected to offline advertising
you're probably best of scaling one/both of the first two options.
organic seo rankings is going to take time, you should spend maybe couple hours a day building links to your site for keywords you think are most relevant.
paid search (sem) is another scalable and faster strategy. it's not 'hands off' and requires you to create (well ok, not requires, I HIGHLY RECOMMEND) some landing pages optimized to each keyword and drive traffic to them. It's a math game, clicks * price per click < your margin * conversion rate. YOU WILL LOSE MONEY. You will also learn and improve if you do this properly and can find keywords where you can meet that basic criteria.
as far as getting links... there is the tried and true for SEO purposes: article marketing, directory marketing, social commenting. But don't forget the real purpose of those links back in the day was to actually DRIVE traffic. I saw some creative ways here about having myspace messages, same with twitter, facebook, etc. The best advice I can give you here is MAKE PEOPLE WANT TO LINK YOU. Create some compelling and interesting content. (checkout mint's strategy http://jasonputorti.com/post/472866002/how-mint-com-acquired...)
Good luck.