What software do I need to make my own toys and games for the web?
Most of the online games you see today are made in software such as Illustrator and Flash.
Illustrator is a vector graphics program that allows artwork to be scaled for the web without loss of resolution (meaning you can zoom wayyyy in without images starting to look crunchy).
Flash is a software that allows you to create actual animations and gameplay that can be seen on the web. You can actually create all of your graphics right in Flash, too. This might be easier for the beginner.
Flash allows you to create simple animations by moving your graphics around on a stage with a timeline (this works a little like moving a ball around on a traditional paper flipbook). Actual games require some programming with Flash's programming language called ActionScript. This is a bit tricky, but there are tons of beginner tutorials online to help you learn. One huge advantage of Flash is that most people already have it installed on their computers, so you don't need to ask them to download anything to view your site.

What if I just want to put a toy or game on my site?
Some sites allow you to embed games on your own site or on your myspace page. Many flash game sites have a little piece of code under their toys and games with the word "embed". Right click in the code box to copy the code. You simply add the code snippet to your page where you have the rest of your copy (and the code will import the Flash from the hosting site). You can try this yourself with this example that creates a virtual Doodle Page. You'll see the embed code right under the toy.