If you run a website the chances are that you will be eager and possibly required by law to have it as accessible to as many people with as many varied issues as possible. It is also likely that this is not something that you know much about and want to do as simply as possible on your existing site.
There exist a number of free online tools that can help you work out where you problem areas lie and explain the basics of how to fix them.
First to get an overall view we would recommend the Nibbler. Nibbler will look at the first five pages of your site and give you an overall score and subscores made up from a very wide variety of factors such as code quality, technology, marketing. Its a good overview and should give you a good idea about any problem areas.
Next is the Colorblind webpage filter. This takes a snapshot of your homepage and lets you apply a range of colorblindness filters to let you check legibility for all types of colorblindness.
Screenreaders often convert a webpage from HTML to plain text and this can be checked at the W3 HTML2Txt site.
Complexity of text can often be a problem and this can be measured by the Flesch Kincaid scale. Read-able.com scans your site and gives you an overall score as well as breaking down by specific sections of the scale and other less used scales like the SMOG Index.
Getting more technical we can make use of HERA. HERA is a tool to check the accessibility of Web pages according to the specification Web Content Accessibility Guidelines(WCAG 1.0). This means that you will get highly specific issues in your code pointed out but will not get much of an overall feel for your sites accessibility on HERA.
Finally you will want to check that your site displays in a reasonable way on all browsers and all versions of browsers that users might have. The easy way to do this is to go to browsershots.org and get a screenshot from what seems like every browser ever made. The site is somewhat slow and may require several result page reloads but it is worth the time investment.
All these tools are useful and can be very good to find places to start but they are not infallible and do make mistakes – particularly on sites which are non-standard. They also do not present a full picture for all disabilities but can with a few minutes work give you a good idea about just how accessible your site is.