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When starting the blender, there is always a cube on the floor. The floor is actually a grid. My question is how to make this grid bigger so that we can measure big stuff?

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I assume you are talking about this grid in perspective view...

That grid on the floor.

Since your goal is to measure things relative to a grid, you can use orthographic view to do that, which makes it easier to construct geometry. Here's how it looks like:

top ortho.

this is the same cube in orthographic projection viewed from above. It is easy to get there. Assuming you are still using the default key mapping (you havn;t changed the keyboard settings) you can get to orthographic by pressing 5 on the numpad and then pressing 7 on the numpad for top view, and 3 or 1 on numpad for other directions.

Hope that helps. If further clarification is needed, feel free to add a comment.

EDIT

So you insert a plain, which is 2x2 initially, as you can see.

enter image description here

now I scale it to 50x50...

enter image description here That just go big. now I get to orthographic view with numpad 5...

enter image description here

And now I switch to top view...

enter image description here

As you can see now, the grid is now spread in all directions infinitely. You can zoom out to see that...

this is the same 50x50 plain.

enter image description here

What you might complain that you can't see the grid inside the plain? Well, for that just switch to wireframe (*by pressing z). Here's how that looks like..

enter image description here

That's one way of getting what you want.

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Thanks very for you help. It is really appreciate if you can help me out of this question. In the first pic in your post, there are 16 * 16 grids under the cube, how could we get, say, 32 * 32 grids? In my case, I added a plain, and scaled its size out to 50 * 50, so that I want more grids to measure it...... –  user3535716 Jul 6 at 11:38
    
Like I said, you can use the orthographic view to measure your plain. Let me show you... –  The Light Spark Jul 6 at 11:59
    
Thanks very much! I got it! –  user3535716 Jul 6 at 12:03
    
I just made an edit to give you an example. Happy modelling! –  The Light Spark Jul 6 at 12:13

You can change the size of the grid to accommodate your needs.

Press N to reveal the properties shelf.

On the Display tab you can change the grid floor number of lines and scale. The left side of the screen will show info on the scale of the units used.

From the wiki:

Lines defines the number of lines that will make the "floor grid" up. If N is the number defined, there will be a total amount of N/2 lines at each side of X and Y axes. For odd values of N, the amount of lines will be rounded down.

Scale defines the distance between grid lines, either in the "floor grid" and the infinite grid.

Subdivisions defines the amount of lines into which the infinite grid should be subdivided. Level of subdivision depends on zoom, in predefined orthographic views.

enter image description here

Other way to deal with large (or very small) objects is changing the scale on Properties->Scene->Units->Scale

enter image description here

Besides the floor grid, Blender has some built in measuring tools that you might find useful.

If you go on Edit mode (Tab), you can access the Mesh Display tab, that allows you to display different measurements (length, angle, areas) of the selected edges or faces of an object.

enter image description here

enter image description here

enter image description here

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