You can Design a website for free using a number of the free website platforms out there.
That link is actually for free blog sites, but you can easily leave out the blog options, and just use the free service for website aspect. Free blogging platforms are dominating the website industry and quickly replacing standard static websites.
Making a website is easy compared to trying to generating website traffic. Blogs are the best free means to generate website traffic to date and this is why they are replacing static service websites. If you want to get any significant amount of website traffic, you are going to have to create a 500 word blog post about once per day. Your blog posts will need to include proper keywords to also.
Design a website with Google Sites
I would recommend using Google Sites if you want to design a website for free. It will allow you to create a website and the option to add blog features if you decide you need one. Google Sites is a free service and offers the ability to add a domain for a small fee when you're ready to upgrade and be more competitive online.