There is a Linux implementation of the Windows API Layer that runs under Linux – called WINE (-see http://www.winehq.org/ for details).
With WINE installed, any applications that were designed to run using the Windows API will access the WINE library for that function instead and so are unaware that they are actually running under Linux!
.. any applications that were designed to run using the Windows API will access the WINE library for that function instead ..
However, do need to check if your software will work with WINE (-the searchable “Wine Application Database” on the URL above is a good place to start) but, as a general rule, anything likely to bypass the Windows API layer (-like state of the art games) probably won't but general purpose applications will. Another useful source of information on WINE is http://www.wine-reviews.net/
Ubuntu does make a version of WINE available in it's Software Centre - just search for the string "wine":
Otherwise, it can be downloaded from www.winehq.org/download
When the installer is run, you'll see a dialogue box containing a progress bar:
At some point, you'll be asked to agree to some EULA licence terms (-for some compatibility fonts):
The installation will then continue:
When it completes, you'll see the following message - click "Close" to end the installation:
If the installation was successful, you should now see the WINE menu under your "Applications" menu:
The only Windows application installed will be Notepad, which can be reached from:
Applications → Wine → Programs → Accessories → Notepad:
The section on Adobe Photoshop gives an example of how to install and Windows application under WINE.