As a start, make sure your code is valid, and, ideally, strict. Then check you are conforming to WCAG guidelines. If you want to buy a screen reader, there is JAWS. However, someone I know uses the IBM screen reader, and seems happy with it. If you go to a site which specialises in accessibility, like accessify, then a friendly forum member may well give you a report.
Download Opera 9 and install the free voice libraries. You can then read out text on any page. (Turn off CSS and images first from the toolbar buttons so it looks and acts like a text-only browser.) Well it's a start...
You can get demo versions of both JAWS and Windows-Eyes which require a reboot after a certain time period (JAWS demo is 40 minutes per session). If you are a designer and you build a lot of sites it might be worth investing in purchasing one. Sadly they all throw up slightly different bugs and quirks so you'll never catch every potential problem. We use JAWS as it's the most popular screen reader on the market, but IBM Homepage Reader is much cheaper and is also a good option.
It is worth testing sites with a screen reader because you will hear problems you never imagined. Better yet, get a screen reader user or several to test your site because they can offer invaluable advice about simple things like naming text links or making your headings and lists easier to scan.