You will want to look for an "Internet Marketing" company. There are many different ways to advertise websites, such as SEO - preparing your website for the search engine results, classified ad marketing, directory listing marketing, article posting, email marketing, and social marketing.
The type of marketing that would benefit your website depends on the products or service you provide, but SEO is a must for ALL websites. Once you are getting traffic directly from the search engines then you don't have to market the website as much. Classified Ad posting will bring you immediate traffic, but will only last as long as the ad lasts. I would love the chance to bring traffic to your website, and show you how internet marketing is the way to earn money from your website. Once a website is built, it will just sit in cyberspace doing nothing if it is not marketed efficiently. Please see my very affordable rates and an explanation of each type of marketing at my website, LouisianaWebsiteServices.com
Links: LouisianaWebsiteServices.com