Even though the game is at beta, it is a lot of fun, and there are a lot of things to do in many different ways. Maps are also generated differently each time you start a new map, and they keep dragging on and on until you run out of hard drive memory. The game plays in 3D using FPS controls.

In the game mode survival, you are basically placed in a randomly generated world complete with beaches, tall mountains, high cliffsides, and creepy caves. 
To see this go here: http://www.youtube.com/watch?v=NszGurDUlHc

There is a night/day cycle, and at night you must defend yourself against monsters, and you can do this in many different ways, an obvious one being fortifying yourself. You can also encounter these monsters in caves, and believe me, they are absolutely terrifying if they catch you off guard despite the blocky style of the game.   You also mine for resources (      ) to make better tools and items which can use to upgrade your house, or whatever else you want to do, like build a roller coaster out of minetracks. You can "craft" a workbench (  ) where you can place your resources in a certain pattern, which will make certain items such as torches which will help you see better in the dark, or armor to increase your HP. There are a ton of things you can craft, all with their own properties, and there are definitely going to be more "crafting recipes" to come later in the future. A fun thing to craft is TNT, which you can use to blow enemies up or mine faster. Or blow yourself up, whatever you find enjoyable.  

An Adventure Mode will also be released some time, which restricts your ability to destroy any block for resource, but instead you play through certain levels trying to complete an objective. Puzzles, Combat, Platforming, that sort of thing.

I was very curious about the game once I bought it, and it ended up being one of the funnest games I have played, maybe due to the sandbox nature of the game. Take my word for it, just buy it. You will get all future updates fore free including.

Yes you can,  Heres a good video.