Off to a good start.
I started making websites the way you made this one. I didn't know the better ways to build websites either, but kudos for being willing to take the first step.
Now, you really can use PSD to slice images for your design. Here are just a few things to consider, though:
* Images mean slower load times. This is the biggest issue. If your website loads slowly, not only will your customers go elsewhere but Google and other search engines will be less likely to rank your site favorably.
* Editing is a BEAST. Does your client come back and ask for green links instead of magenta? No problem, you just have to re-slice out every image. And their hover state. Do this about the 5th time, and you'll see the downfall of this method. If you code the site using best practices, this would only take a second (literally) to change.
* Blind people can't read images. Neither can Google. A lot of the magic behind making sure people are visiting your site is to make sure that search engines can tell what your site is actually about. If people don't see your site, they can't buy your product, you don't make money.
* Images scale, but they don't resize. If someone's viewing your website on a smaller screen (say, a tablet or mobile) they get treated to a site that's much too large (or small) for them to use correctly. Text is built to overflow nicely by default; if you put it into an image then you lose that behavior.
If you're looking for a good place to start with learning the proper ways to build websites, I'd recommend
Codecademy. Their short, easy lessons will show you the ropes.
Best of luck!