First, you need the sphere. I suggest you start with a cube. This way you get almost evenly spaced quads all around the globe.
Add a subdivision surface modifier to the cube and crank up the view subdivision to 4. Click "apply". It should look like this:
Go into edit mode with Tab.
Go into Mesh select mode: Vertex with Ctrl+Tab and selecting Vertex.
Select everything. Hit A until all vertices are orange.
Make it a true sphere. Hit Shift+Alt+S. Type 1 and then Enter.
Use the knife tool to cut out pices of the sphere. Start the knife tool with K. Click around until you are satisfied. Finish with Space.
Go into Mesh select mode: Face with Ctrl+Tab and selecting Face. Right click all the faces you have cut out. They are still part of the big sphere. Hit Y to make them separate from the sphere. Hit E to extrude them out from the surface.