If you are simply designing then look firstly at a few key areas:
Who is it being designed for?
Are there any special requirements?
What is the theme? Is it sombre, is it designed to intruige etc.
Who is the audience?
From these, bring together a brainstorm and pick the best bits, submit them to the person it is being designed for (could be yourself) and see which bits they like, get it peer reviewed and then draw up your final design.
You might find it easier to do it on paper first instead of wasting time on PhotoShop, GIMP or another similar program.
If you need programming specific help then by all means come back with seperate questions.
If you are interested to learn web designing then you have to first knowldege of efefctive web designing software like Dreamweaver,Photoshop,flash etc. Using best design software you can design website more attractive and valuable.
Unfortunately I would disagree with using w3schools.com, it doesn't teach you the best practices and in the long run you shall end up making a lot of poor errors.
Instead I would recommend the official resources which can be found at w3.org
Furthermore, you don't need to have a lot of expensive software as suggested by madelinekim, Notepad/Gedit/Text Edit are all perfectly fine if you know some HTML and CSS, or if you want a WYSIWYG (What You See is What You Get) Editor then a cheap one from Amazon is a good place to start instead of spending £200.
If you plans for design a website for that you need good knowledge of programming language and also need good graphics design knowledge. As per the web design concern i would like to say that to make your website design very effective and customer attractive,provide good navigation control in the website,fast access time and make it user friendly.
To design a website you can use a content management system. There are many content management systems available on web. Some of the different kinds of CMS that are Joomla, Wordpress, and Drupal etc. In my opinion, you can use wordpress for designing websites. There are tons of themes and plug-ins you can build very attractive and good looking websites.
The first thing that you want to put into consideration is the difference between designing a website and developing a website. This is because sometimes the people who design are good at beautification of the site, but may be poor at the coding part. So by the fact that you are asking for "designing", I am thinking that you have already developed it.
So, to cut the story short; all you'll need to do is to identify;
1. Whom you are designing it for
2. What are the preffered colors by the client
... and so on.