They just changed the material setup to a node based one like what you get when you press the use nodes checkbox in the old default render engine (blender internal). First select the object, open the shader editor (node editor in 2.79), then click Add menu > Texture > Image Texture to add a texture node (pressing shift + a opens the same menu under your mouse):
Next set the node to the texture you want. Clicking new creates a blank texture that has to be painted in either the image editor or 3d view:
Finally, click and drag the yellow dot on the right side of the image node to the yellow dot labeled base color on the left side of the principled bsdf node. This tells the shader to use the texture you just set for that attribute:
This node based shader system is more flexible than the old one. You can even recreate any layer based compositing setup with it (including photoshop style compositing). I posted some examples of how to do this in other, older topics. I recommend taking a look at them since I like to be thorough when I talk about this sort of thing:
Yes, they have made a lot of changes, but the bulk of the program is the same. I think the main thing that has you confused is the new default render engine. They had to delete the old one because the codebase for it was a mess (written in the mid 90s). Eevee, the new default engine, uses more modern concepts for building materials which aren’t compatible with how the old engine worked.
You have me really confused with these statements. In both 2.80 and 2.79 Ctrl + MMB zooms into your object and Shift + MMB moves to the left or right of it. They have only changed a couple of things concerning navigation in 2.8 (alt + F was changed to alt +MMB and shift + F was changed to shift + ~). I think you picked one of the alternate keymaps for 2.8. Make sure you are either using the default keymap, or the 2.79 keymap. Edit menu > Preferences > Keymap button:
