There are three major ways in my opinion to accomplish this and they all play hand in hand.
1 - Increase search engine rankings. This is probably the single most important thing you're going to want to do and it almost happens more as a side effect of everything else. Search engines are the world's portal to the world. You want to be somewhere on that portal obviously. The biggest advice I can give in terms of this goal is "Content is King". The more content you have (not just a bunch of crap) the better off you are. You need some meat for the search engines to grab ahold of. This will greatly increase your chances of getting those sweet "organic" hits.
Another key ingredient here is link popularity. You will need to gain recognition around the internet to build repore with the search engines. The next few items on our list will help with this. The only other important peice to this one is just make sure your website is of high quality. Nobody knows exactly how google gets the results it does as the search algorythms are secred, however we do know they they generally pull very good results. Make sure that your content is quality and relavent information, and keep search engines in mind when you're creating traffic. Dont forget to use google webmaster tools to add your site to google's index. While your at it using google analytics can also help identify what keywords are working well for your site so you can try to target those visitors more aggresively.
2 - Get listed on as many sites as possible. Depending on what type of website you have, there are bound to be plenty of directories, top sites, coupon websites where you can list your promo codes, shopping repositories like google products, shopping.com etc. etc. etc. Find as many way to get your site included and listed on as many different services and websites as possible. This will also help your link popularity and get you more search engine traffic.
3 - Back on the 'content is king' kick, publish something regularly that can be indexed by search engines, but also followed via rss readers like good reader, or services like feedburner. A good example of this is keeping a regular blog. Make sure you post new articles at least twice a week and you will be surprised to see that people might just be interested in what you have to share. This can be a good way to promote your other website like I'm gonna do right now:
See how that works?
4 - Paid traffic. Make sure you go with reputable sources, not some company thats going to throw you 10,000 impressions from popup advertisements generated from spyware! Go with targeted ads from services like google adwords. Another great one is facebook! You can really narrow down the potential viewers to exactly who you want to target, right down the their marital status. They can certainly work wonders and get you truly interested visitors.
Last but not least, if you do end up getting gobs of traffic, dont forget to send me some. I love traffic. =)