This how-to shows how to get Game Maker running best. It assumes you have Ubuntu 10.10 Maverick Meerkat installed. There may be different procedures for different versions/distros.
Make sure you've updated Wine to the latest version(1.3.17).
If you haven't, copy and paste this in Terminal:
sudo add-apt-repository ppa:ubuntu-wine/ppa
sudo apt-get update
sudo apt-get install wine1.3
The last command should show "wine-1.3.17".
To make Game Maker run correctly, make sure that Internet Explorer 6 is installed. I don't think the other versions of IE work.
To do so, open Terminal and copy and paste the following:
sh winetricks ie6
sh winetricks directmusic
sh winetricks dsound
sh winetricks d3dx9
sh winetricks mono210
It will open the installer for IE6 which then allows Game Maker's News screen to load. Then it installs directmusic and dsound to allow sounds to play. It also installs all the DirectX tricks needed for Game Maker to run correctly and the .NET compatibility.
After that, instead of installing Game Maker like normal, go to Uninstall Wine Software in WINE's menu. Then click the first button, browse to where the installer is and install Game Maker like normal.
After following the above steps, everything seems to work fine, but when running games there is some lag. Because all these tests were run in VirtualBox, the lag and other problems may be nonexistant in an actual installation.