I am trying to upload an image for a contest thats over in 2 days so this is an emergency!!! I need to upload the picture. I've tried changing the resolution and resizing it to meet the requirements but either the file is too large or the image is too small. I cant seem to meet the requirements!!! Somebody please HELP!!!

Very quick guide for saving for web. Press ctrl alt shift and S, or File Save for Web. If your saving a normal picture (not a gif) make sure box 1 says JPEG.

Click on the arrow in the quality box (2) and a slider will appear move this slider to adjust the quality of the picture.

The file size appears in the bottom left of the picture (box 3)

Click save and you’re done.

If you use photoshop and want to save your pic optimal for a given filesize, you should indeed make use of Save for the Web (ctrl-shift-alt-s) as Serps pointed out.
In the save for the web-dialog you can push the little arrow to open up a menu:


There you click optimize for file size, which popups a second dialog-box:



Fill in your maximum filesize and Photoshop wil return the most optimal settings in the save for the web-dialog.



Edit:
Links to my images were broken for a while. So I've put them elsewhere. Thanks to http://imageshack.us/ for hosting.