To make this work make sure that you know where the minecraft.jar file is and download an image for the desktop icon. (You can download the jar at http://www.minecraft.net/download. I used the icon at the following link http://fav.me/d36xhh8)
The first thing you need to do is create a .desktop file on your desktop. Copy/paste the following into your favorite text editor:
Exec=java -jar <Directory>/minecraft.jar -Xms 4096M
for a full explanation of what all this does see Anatomy of a .desktop File.
Make sure to replace the bolded values with the appropriate directory (in place of directory) and memory allocation (in place of 4096M - 4 GB of RAM dedicated). Furthermore, if your image name is different make sure to replace it.
Save this file in your ~/Desktop/ directory with the filename Minecraft.desktop
The next thing you need to do is make sure that the file is executable. The easiest way to do this is right click on the desktop icon, select properties -> Permissions and fill in the box next to "Allow executing file as program". Alternatively, open up a terminal, cd into the Desktop directory, and type the following comand:
sudo chmod +x Minecraft.desktop
When you do this the icon you selected should be visible on your desktop, and double clicking it will launch minecraft.