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How hard is it exactly to use the new Game Maker?

How much time would it take to learn Game Maker enough to create a basic game with it?
Depends what you mean by basic.
You can probably get a handle on everything in a few hours just by going through all the tutorials that it comes packed with.

If you want to get into scripting that depends on how much experience you have with programming. But again there are plenty of tutorials that are easily accessible.
Krakenskin Leather Works, my Etsy store.
LordVanya, my art page.
FundamentalEssence, my game development page.
I have absolutely no coding experience haha xD
No problem all the basic functions you'd need to make a simple game are available in the drag and drop system.

Just follow the tutorials and you'll be good to go in a day. When you want to start making more complex things there are tutorials on scripting and a very robust support network at the Game Maker Community Forums.

And you have any questions feel free to pm me.
Krakenskin Leather Works, my Etsy store.
LordVanya, my art page.
FundamentalEssence, my game development page.
Besides Vanya offering you help if you'd like to see the coding side and get an idea of what it entails This guy makes really good game maker tutorials.
Thanks guys!
I'd also like to add that with Game Maker the difficulty is exponentially related to what you're trying to accomplish. For making 2d games such as space shooters or platformers it's pretty great. However, as soon as you start dabbling in 3D to make something like an FPS you're probably gonna find the engine rather annoying to work with. When I used Game Maker four score and seven years ago this book helped me quite a bit, so maybe look into stuff like that if you're the more reading based learner.

If you're interested in making really basic games for free, then there's always Scratch. For first time programming it's worth a look. It also comes with an animated cat!
Well, pretty much ALL 3D game engines are better for 3D than Game Maker. That's just common sense. Unity 3D is one that's very friendly for beginners, though. Unreal Engine 4 as well, although a little bit more advanced and therefore a little bit harder with some aspects.
Feel free to visit my website/blog - it's updated rarely, but it looks pretty cool!