It really depends on what exactly you want your website to do, how complex you want it to be, and how much time you want to devote to putting it together.
If you want a website that is generally static, I would suggest a service such as Wix. Wix, and others, are services that allow you to quickly put together a decent-looking website using a drag-and-drop interface. As far as these services go, Wix is the best one that I've found -- not that I actually use it for anything -- as it has a large selection of templates, a simple-to-learn interface, and it integrates flash technology well. These sorts of quick, drag-and-drop website creation services are the most basic option for quickly setting up a website.
If this doesn't suit your needs, you may be looking for what is called a content management system (CMS; link is to Wikipedia.) A CMS is essentially a program running on a web server that allows you to create, publish, and edit content. Blogging services are a simple form of CMS with a single type of content (a blog entry). There are three major content management systems in the industry:
- WordPress - The most popular CMS. Originally it was just a blogging system, but its capabilities have since been expanded to allow for all types of content.
- Joomla! - More complex than Wordpress to set up, but also popular. Has been a full-fledged CMS longer than Wordpress, so you may be able to find more plugins that suit your needs.
- Drupal - Of these three, the most complex and hard to learn. But it also offers the best security of these three solutions. (The White House website is powered by Drupal. Take that as you will.)
There are many web developers out there who will build you a Wordpress/Joomla!/Drupal site from scratch or from templates, and who will charge a decent amount of money -- but not as much as someone who you ask to roll a complete custom solution. Like I said, though, you weren't too clear on your specific needs, so it's hard to give a more concise solution. If you have stringent security needs, existing databases (with complex schemas), or are trying to implement a very complex solution (like a game or app), you may need to go with a professional web developer instead of one of these options I've mentioned.
Disclaimer: I am a web developer. Keep in mind, I am essentially giving you advice on how to put myself out of business.