Canvas and bowling ball I'm having trouble understanding the basic model for how matter bends space. The classic illustration is the canvas and the ball but that model needs a reference frame where one can define a downward direction to work. For the life of me I can't figure out why matter just doesn't "sit" in space.
I'm sorry this question isn't better formulated, maybe someone can point me towards a video or something?
I'm having trouble understanding the basic model for how matter bends space.


No wonder, because it doesn't. It curves spacetime. But spacetime isn't the same thing as space. See this Baez article: "Similarly, in general relativity gravity is not really a 'force', but just a manifestation of the curvature of spacetime. Note: not the curvature of space, but of spacetime. The distinction is crucial". Space isn't curved where a gravitational field is. Instead spacetime is. 


  The classic illustration is the canvas and the ball but that model needs a reference frame where one can define a downward direction to work.


That's right, it uses gravity to "explain" gravity, so it isn't ideal. However there is a way to understand it, and IMHO it's simpler than you think. 


  For the life of me I can't figure out why matter just doesn't "sit" in space.


It does just sit in space. And it causes gravity because it's a concentration of energy that "conditions" the surrounding space. It alters it, and this alteration diminishes with distance. Remember the stress-energy tensor, remember that stress is directional pressure, and think of matter as exerting an outward pressure in all directions in the surrounding space. Something like this:


Earth image courtesy of NASA, lines drawn by me 

Then see the Einstein digital papers, where Einstein said a gravitational field is a place where "space is neither homogeneous nor isotropic". This inhomogeneity isn't linear. You can plot it, using say optical clocks dotted throughout an equatorial slice through the Earth and the surrounding space. You plot lower slower clocks as lower down in a 3D image, and higher faster clock rates higher up. When you've finished your plot looks like this:


CCASA image by Johnstone, see Wikipedia 

The upper image is a bit like looking at the lower image from underneath. But anyway, your plot is curved, and you made it using clocks in space, so we can say spacetime is curved. Note that whilst we started with a two-dimensional equatorial slice and ended up with a three-dimensional curved plot, there is no extra dimension in any real sense. All we're depicting is the "coordinate" speed of light. This might sound unfamiliar but again see the Einstein digital papers: "the curvature of light rays occurs only in spaces where the speed of light is spatially variable". Light doesn't curve because your plot of optical clock rates is curved. It doesn't curve because spacetime is curved. Einstein never actually said that. He said it curves because the speed of light varies. Hence the tilted light-cones on John Norton's course. Light curves wherever your plot isn't flat. Where the speed of light varies. It's actually rather like sonar:

 

Image courtesy of FAS and the US Navy, see course ES310 chapter 20