Again, Unity will let you do that. Your task now is to FIND a pre-made template and take it from there. Their new 2D version of their editor has a nice intro video you can watch here (it's very, very good):
http://www.youtube.com/watch?v=4qE8cuHI93c
What you REALLY want is something both GameSalad and YoYo Games' GameMaker offer. However they end up costing you a lot more in the end, and they don't give you much room to branch out, and you need to pick an editor that does to begin with so it's easier once you start trying to make your own mechanisms/gameplay that are not possible in those other programs.
Try out one of the visual language plugins (or at least start comparing them all, find trials, etc) once you get Unity setup. Follow a simple tutorial and you can use that knowledge to make something else right away then and there.
Here are some tutorials from Unity's forum even:
http://forum.unity3d.com/forums/23-Teaching
Trust me. Do a tutorial on Pong and you will then KNOW how to do the following:
- Scoring system
- Walls/boundaries that change
- Small collisions
- Movement of objects with different properties
- Destroying objects
- Basic menus
- Using images/shaders
- How to program gameplay
Learn how to make a proper game by actually doing it. Pong will take you 30 minutes to a hour, and again it's knowledge you can take immediately and make something else with. You might have to read a little more into it to make a platformer, tower defense, etc, but again, the basic knowledge is now there for you to use.