This is my development environment:
Note this article, from Bloomberg:
In order for python scripts to call Bloomberg API functions, the libraries distributed as part of the Bloomberg C++ SDK must be available to the Python interpreter. Step 3 of installation, above, provides system-wide installation of this library. Linux/Solaris/*nix users without system-wide installations must set the LD_LIBRARY_PATH (or DYLD_LIBRARY_PATH on Darwin/MacOS X) environment variable to include the directory containing the blpapi3 shared libraries. Windows users may need to set the PATH variable to the directory containing blpapi3_32.dll or blpapi3_64.dll. (Note that Windows users with the Bloomberg Terminal software installed already have versions of these libraries in their PATH.)
So what I did (very similarly to Keng Onn's answer) was:
Download the C/C++ lib for Windows
Extract files from blpapi_cpp_3.8.8.1.zip (or similar)
Copy blpapi3_32.dll from the bin folder and paste it anywhere safe
In my case, I pasted it into C:\Python27\Lib\site-packages\blpapi
Add this route to your Path environment variable
Click "Start" / Right-click "Computer" / Properties / Advanced System Settings / Advanced tab / Environment Variables
Double click "Path" under "System variables" list
Add a semicolon (;) and your path as seen below
For me: C:\Python27\Lib\site-packages\blpapi

Now it should work just fine for you. Hope it helps.