First I did a quick Google image search using the key words "map of Earth" then copied one that was in square format.
Second, I added a UV Sphere then unwrapped it with the following settings.
I then drag and dropped the image from the hard drive folder into the UV image Editor and scaled the UV Islands up along the Y-axis to get the image to fit better.
I have Blender Rendering set to Blender Internal and there are some settings on the right that will help you to see the image under the Shading Tab
Now I went back to Object Mode, then clicked over the sphere model to position the cursor onto the surface and added a plane. In edit mode, I merged the vertices into 1 by using the keyboard shortcut Alt+M and selecting At Center.
In the image that follows, you can see one little orange point hovering near the surface of the textured sphere.
Now look at the bottom of the 3D View and activate the magnet Tool
You can use Ctrl + mouse click to quickly extrude out new vertices all along the continents on the reference model. (I wrote 'mouse-Click' instead of left-mouse or right-mouse because people use different defaults for the right and left click)
After you have the outlines done you can start manually choosing sections and adding in faces using f Make Face.
You'll have to be careful about this part because the model is curved and making one big face will cause problems because it will be a flat surface trying to fit a curved profile. Try and make the faces in smaller chunks.
After the continents are filled in, you can use e Extrude to give thickness to the model. Or you can use the Solidify Modifier.
Now you can delete the reference model with the map on it and replace it with the model that has the Wireframe Modifier on it that is shown in one of the other answers.
If there are any steps that you have problems with then come back to this site and start a new Question for that specific area.
Update based on comments.
To make a height map, I used the downloaded picture of Earth mentioned above and loaded it into GIMP and used the Color/Area Select tool that most programs have and selected the ocean color which selected all the ocean area using default settings. I then flood filled this area with black. Then I used color contrast to get the following image.
Now I added a second set of UV Coordinates using the following panel,
I did this because the coordinates for the Spheres poles did not fit into the image area properly and I wanted to paint the poles black to hide the errors that were showing up there form bad mapping.
Then I added the height map made in GIMP as a material texture and baked it to the new coordinates.
Then I added this in as the material texture and used texture Paint mode to paint out some of the other problems.
Now I added this texture in as a height map for a Displace Modifier which came after a Sub-D Modifier and at the end I added a Decimate Modifier with the settings in the following image.(You can right-click the image and choose 'View Image' if you can't see the settings from the preview)
Now I applied the modifiers and and used Circle Select to select all the ocean faces. Once they were all deleted I was left with the following.
Next I added another Decimate Modifier to clean up the mess and reduce the poly count down to something easily manageable. I was mostly concerned with cleaning the jagged edges at this point, this produced the following.
Next came the Shrink Wrap Modifier with the following settings.
And with a simple lighting setup, the final render.
You could use Texture Paint to paint in dividing lines then bake a normal map from this to get a bit more detail. That would be far more straight forward than actually creating geometry to divide various countries, states, provinces, etc...