How can I make a dialog window with transparent background which looks like exactly like this:
With transparent background, so the Aero glass color is white.
If you hover your mouse over the picture, you may see checkered patterns, which is transparent, so the Aero glass can see through the checkered patterns. (Note: Please do this in the link above.)
How can I do this like the Aero glass see through the checkered patterns above?
You will want to use one or more Layers, partial layer transparency (e.g., by using a grayscale Layer Mask), and save in a format that can carry transparency such as PNG.
Note that you will never be able to achieve the blurring that Aero Glass does to things that show through, so the effect will never match Windows very well. With Windows 8 there will be no more transparency of individual windows, by the way - just partial transparency of the Taskbar.
You can determine the extent of the transparency and the color used, in order to learn to match it, by loading the very PNG you put up in your post above into Photoshop (CS5 or newer), then do Layer - Layer Mask - From Transparency.
What is your intent? To create a Photoshop design that uses partially transparent layers? To display partially transparent things in a web browser? If so, I have already told you exactly what you want to do.
You're going to need to go research how layers and transparency work in Photoshop I think. That's a bit beyond a Q & A forum to teach.
Layer - New Layer, Color: X None. That creates a new completely transparent layer on which you can paint things.
Select something with pixels in it, Edit - Copy, then Edit - Paste over whatever layers are there. That will create a new layer with transparency all around the pixels you copied and pasted.
To make a layer mask with which to make parts of a layer transparent, Layer - Layer Mask - Reveal All, then paint black on the Layer Mask. Gray makes it partially transparent.