Simplest way of accomplishing what you want:
Create a new cube as you usually do. It will show the vertices (little points on the corners. Yellow means they are selected ). This is edit mode. Hit the tab key. This is object mode. It’s wireframe should now be pink with no vetices showing (still selected). hit the letter A. It should now be black (unselected). Still with no vertices showing. Move your 3d cursor where you want a new cube to be by pressing the left mouse button in the 3D window at that location. Create a new cube as you usually do. Blender will automatically put the new cube into edit mode again. Press A to switch back to object mode. The new cube should now be pink. You can right click back and forth on the cubes to select and deselect them. Press A to select both and deselect both (toggles select/deselect all). Now select one (RMB) and go to materials buttons (F5). Use the add new button under materials. Use the color sliders to make a new color. When you are happy select the other cube (RMB) and make a new material the same way as above. Hitting Z will toggle solid view on and off so that you can see your material applied to the cubes.
Things to remember: Two basic modes in mesh editing (there are other modes that aren’t that important at this point) Edit and Object. Tab toggles between them. Edit allows you to manipulate the shape and form of an object on a vertex/face/edge level. (that’s why in edit mode you can see the vertices and select them individually. Object mode allows you to manipulate the object as a whole (ie. assign material, resize, rotate, move around in scene quickly). If you add a mesh while in object mode it becomes a seperate object. This makes isolating it from others for editing and positioning and assigning materials to it etc. easier. If you add a mesh while in edit mode it will become part of the current object. Try it and then tab into object mode. These two meshes will select, scale, move, etc. as one.
For what it’s worth as you learn the more advenced tools you can join and seperate objects, assign materials to just certain areas of objects (groups of vertices) isolate meshes of the same object while in edit mode, apply scale, rotation, location changes in edit modes as well as object mode, etc. Blender offers a huge amount of flexibility in this area. As you progress you will develop a workflow that suits your needs. The best way to learn (aside from reading the docs) is to keep in mind what I said in the preceding paragraph and just experiment with the tools in different modes. Maybe tackle a tutorial or two. In the mean time, keep one hand on the keyboard, the other on the mouse and chin up. It gets easier!