Everyone has one these days. Well, almost. Many of them are very good. Many more are bad. No one intends to have a bad site, but as in any other undertaking, uninformed intentions may miss their aim.
First consider, what is the purpose of the site? This may seem obvious to you, but on the Internet your potential audience is the whole world. What part of that immense, varied mass of humanity do you hope to reach, and why, and how can you make your site appeal to them? Is it intended to communicate and inform, to entertain, to impress others with how great you or your products are?
Talk it over with others, do some research on the web. Think about sites that have impressed you one way or another. Put yourself in the place of a person who might be interested in what your site could offer, and apply the Golden Rule. Also, remember that other people are not using your computer. They have their own hardware, software, and viewing preferences, all of which will make a difference in how your site appears to them.
How will people find your site, and will it be what they are looking for? The Web is one huge dating service. Just having a nice name and a pretty face won't bring traffic to your pages. Reciprocal links are one way, and advertising, but they are limited. Only those who find a link and happen to click on it will come.
Search engines serve anyone who can type in a few words. The more searchable words that can be found on your site, whether in readable text or in the invisible (to the viewer) header of a page, the more likely it is that the right person will find the right site.
Who will maintain the site? Information needs to be updated, errors corrected. Links need to be checked. A stale site full of dead links loses return traffic. "Oh, that old thing—bleh! Nothing but dead links, and nothing new since last year."
Structure of a site matters too; not just the navigation links, but organization of the actual files on the server. A little planning before throwing it together can save a lot of headaches later. Will you be able to pick one cryptically named image out from a thousand others when you need to change something? Will you run out of space because you have several hundred unused files but don't know which is what and don't dare delete any?
If a site is intended for people of all ages and abilities, will all of them be able to use it? Though it is not possible to deliver perfectly equal content to all users, accessibility is an important consideration, unless your site is aimed only at the young and perfect. Don't forget that even among the healthiest of the population, nearly a quarter of all men have some degree of color-blindness.
back to contentsRead the first part first. 
Then find out what that person or company thinks is important. Ask yourself whether they are more interested in getting your money now, or whether they will be with you for the long haul. Do they try to sell you a package that doesn't fit? What about maintenance?
Apply the same criteria that you would to someone who is trying to sell you a car or insurance. Get what you need, not what is most profitable for someone you may never deal with again. Beware efforts to push trendy technology (which may not be suitable for your intended audience or purpose). Start with the basics; you can always improve on something good. Repairing a failure costs a lot more in the long run.
Anyone who can buy a few pieces of expensive software can set up as a "web designer" and try to recoup the cost. Expensive tools do not cure fools.
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Do yourself and your viewers a big favor—learn at least a little about how web pages work. It isn't hard to learn a bit of basic HTML (HyperText Markup Language). Just for starters, you will see better why it is necessary to have a good title for each page, not "blank" or FrontPage's ubiquitous "New Page 1." Worse yet is a two hundred word description of the site that properly belongs in a Meta tag for the benefit of search engines.
This is not the visible, large text title that you see at the top of the page as displayed in the web browser. The title I am referring to here is in the page's head section, between the <title> and </title> tags. It is only seen by your viewers in the titlebar at the top of the browser's window - and one other important place.
A page title becomes the name of a viewer's bookmark or "Favorites" link. Make it meaningful in as few words as possible; it's a road sign, and drivers on the Information Highway are in a hurry.
Sure, there are plenty of (mostly expensive) WYSIWYG (What You See Is What You Get) page creators. You can even make a web page with a word processor (MSWord et al). Unfortunately, what you see is not necessarily what the other person gets. Besides that, what you see may be a very small item compared to the bloated, redundant, ridiculous underlying code that most of these things create. A page made in Word will be ten times the size in kilobytes as a page made with clean code in a text editor.
When a site is designed only from the viewpoint of outward appearance, the creator can easily forget that other people have different computers, different monitors, different browsers, different settings, and different Internet connections! Actually, that is a problem with too many "Professional" designers as well as amateurs. But let's not go there just now.
A little knowledge of the mechanics of design, and a little testing with other computer setups and web browsers will go a long way toward broadening site appeal and usability. Ask other people--not your close friends and dearest relatives, if possible--to "test-drive" your site before sending it out into the wide world to make its fortune. Can they find what they are looking for? Does it look as good on their screens as you thought it did on yours? Make sure the Emperor really has some clothes on. 
Check for spelling, grammar, and punctuation errors too. Even Google notices—researchers have found that sites with fewer typos rate higher.
back to contentsOne little word says so much. Content goes hand in hand with purpose and purpose is everything. The first page of a site should tell what the site is there for, and what it has to offer. People want information, now. Search engines thrive on textual information. They can't read pictures.
Can people find their way around easily, with as few mouse-clicks as possible? Can they find their way back to where they started? Do they have to backtrack too far to get to another section? Are your links usable if someone turns off javascript, Flash, or image display for some reason? Many do, to avoid ads, speed up their browsing, or even for security. Even appearance matters here: a consistent page design keeps links where they are expected, and tells people that they are still in the same site.
Did I mention that people on the Information Highway are in a hurry? Not all of them have the latest technology. Even those who do sometimes find that it isn't all it's cracked up to be. There is more and more web traffic, and bottlenecks occur. An eighteen-wheeler web page can still cause a traffic jam.
Don't try to put all your content on one page, either. People not only want a page that loads quickly, they don't want to scroll half a mile. Divide and conquer. Search engines like linked pages too. 
The faster a web page loads, the more likely it is that a person will stay to see more. Just because your counter or server log says that someone "visited" your page doesn't mean that they stayed there. They may have backed off in disgust and made a note never to return. 
W3 org - THE source for HTML and CSS guidelines
Web Accessibility Checklist - find out what matters
A list apart - very informative site
W3 Schools - an excellent place to learn
Webmaster World - Site full of useful information, discussion forums
Search Engine Showdown - Information about search engines, comparisons, links