sadly it's not that easy. that's the one thing you need to understand going into this, is to not underestimate game development. common misconception.
firstly, you need a platform on which you will create your 'game'
there's a lot of free engines out there that you can use, but still require a lot of programming experience to get em on the go, not to mention the tools that are used to utilize these engines can be a bit wacky.
the best thing i think you can do if you really are interested in this, is go with a game that has a good sdk(software dev. kit) and just work from there. it may not be entirely yours, but, should at least allow you to work things out and get shit on the go.
i can't think of any platform that'll actually support google sketchup. GTK radiant is supported by a lot of platforms/engines... however, it's pretty useless if you have no assets to use (ie. textures/models/entities).
if you REALLY want to see what actual modelling is all about, try downloading a trial of a popular modelling platform ie. XSI, 3ds max, maya etc. etc.
blender is free, but, i hate it. then again i learned with 3ds max, so.