To be honest you will be hard pushed to have a successful business in web design if you don't know how to code or graphic design. Your customers will want you to give a true reflection of their business and design the site so that it converts.
An ugly design will give an unprofessional image of the company you are hired to represent, no matter what others may say. It is all about effective branding, so you could do with studying marketing and branding to see what works and what doesn't.
Without coding knowledge you will be unable to tweek the site to the customers requirement. You also need to consider cross browser compatibility, css, ssi, compliant coding and what aspects can effect the visitor experiance (ie if you have javascript links and the client has java turned off they won't be able to navigate through the site, users and search engines don't like flash websites etc)
Then you have the other areas, knowing how to market the site, knowing how to build a site so then if can be marketed effectively and safely, knowing how users naturally roam through a site so then you can build it to convert and lead the visitor in the right direction through the site.
Also you will need experiance of working with popular CMS and ecommerce scripts etc.
Unfortunatly there is a lot to learn, I have been in the biz for 8 years and still learn something new every day, I have to, to keep on my game and a step ahead. Unfortunatly it takes a lot of work to master the diciplines you need to create an effective ebusiness for someone. I started out purely in one area (seo) back when I entered this market, working white label for other companies after 6 months training and study. I only moved across to other areas as my skill and knowledge increased (although I was trying to install cgi scripts and edit design within the first week). There is no way I could have worked on a whole project from start to finish when I first started.
It is great you want to learn about website design and if you want to learn more I would suggest having a look at some websites that work and look good, noting down what it is you like about them, maybe downloading some pre-existing templates and having a look at how they are constructed. I would recommend dreamweaver for constructing a html design, editing coding, CSS etc. Go in and have a play, this is the best way to get to grips with the standard design stuff, the rest you have a lot of studying to do and it will take years not weeks to master until you are ready to set up a effective web design company.
However, if you have a business that includes webdesign as part of the the business you intend to create your time may be best spent elsewhere and you can always partner with an experianced developer/designer/marketer for the rest!
I don't want to disparage you from following your dreams, however I did want to let you know what you have instore for you, so you can have a true reflection of what lies ahead and what you need to do, should you decide to take this path.
Whatever you do, I wish you the best of luck.
