If you have recently had a website designed then you will need to consider who you are going to promote it when it goes live. The search engines can take a little while to index all of your pages, and even when it does there is no guarantee that you will rank high enough to attract a large number of visitors. To make your website rank higher you need to have great SEO behind it and constantly be updating the site to not only improve the rankings but even to maintain them.
A good way to get traffic straight to your website is to use paid for advertising such as Google Adwords or Facebook ads. These can go live almost instantly and if you have set the campaigns up correctly, you can get the right people to your site the day it goes live. When setting up any paid for advertising you need to know what you are doing as errors can be costly and you may find that your budget gets used up quickly with little qualified traffic to your site.
Social media is another good way to promote your new site and best of all, most of it is free. You will need to be able to build up a following of people to post to and also find relevant groups in which you can post.