Here are the steps to download the free TI-83 simulator:
 
 
2.  Click on "Download".
 
3.  Read the license and accept the legal stuff.
 
4.  Click on "TI-83 Plus SDK".  This will download the program.  (4.2 megs - a fast connection is nice.)  Be sure to remember where you SAVE the program since this will need to be installed.  ("save" rather than "run" at this point.)
 
5.  Install the program using all the normal "next" prompts.....when done it will ask you to reboot.  Be sure to do this to finish the install.
 
6.  After you reboot - there is a new icon on your desktop called "TI-83 Plus Flash Debugger".  To activate this do the usual double-click to open the program.  When the program opens - under the FILE menu, choose "New" and then choose the calculator of your choice (usually TI-83 Plus Silver Edition) followed by OK. 

Another window comes up - choose from the top menu Debug (even though it is not highlighted) - from there choose "GO". (Or you can choose the "arrow" under the  word "View")  The simulator opens up and you can use it like a regular calculator.  You can minimize the other open windows to get them out of the way and you can move the calculator by dragging the blue bar at the top.  You cannot resize the calculator.

7.  Additional information is available at the website above if you have trouble or want to learn about running TI-applications on the simulator.