You can download the program for free at www.gamemaker.nl The "nl" stands for the Netherlands. That is where the creator of Game Maker lives. Bill Kerr from Australia wrote a tutorial that teaches people how to make Space Invaders.
Here is your Space Invaders Information:
This is a game of Spaced Invaders. You need to download the following 2 links for the tutorial: To download them right click (middle finger) and select "save target as."
Document 103 This is the tutorial
spcInvdrs.zip These are the sprites and sounds.
http://www.mindtools.tased.edu.au/gamemaker/mazegame.htm
Make sure to save the game in your Game Maker Folder.
These are links to tutorials from other people.
Here is a tutorial on how to shoot:
http://www.mindtools.tased.edu.au/gamemaker/shooting.htm
Working with scores and lives.
http://www.mindtools.tased.edu.au/gamemaker/scoring.htm