Traffic from search engines will take awhile since your website is new.
But in the mean time while you're waiting for search engine traffic you can use these other ways of getting some traffic to your website.
1 Post On Forums
Find forums that are related to your websites niche "Topic" sign up for the forum and post some useful content on the forums.
Most forums will allow you to have a link to your website in your signature and in your profile.
Keep posting daily on forums. My forum http://webmasterbabble.com allows users to post links in there signatures and you can also post your website in the reviews section to gain traffic and get feedback on your website.
2. Make Youtube Videos.
Make youtube videos relating to your websites topic and then put your websites address in the video itself and link to your website in the description box.
3. Use social Media.
Another good way of driving traffic to your website is by using social media websites such as Facebook and Twitter.
Put your website address in your twitter profile and follow other users. They will in turn follow you back and you'll eventually gain other followers.
Don't pay for followers as those will most likely be bots and not real people. Or at least not real people that are interested in your twitter account.
Follow and let them follow you naturally.
It takes time so be patient.
Keep working on your website and you should see the fruits of your labor sometime down the road.