I prefer use the portable version of Notepad++ so everything was aimed to keep that still running on an external HD.

Its assumed you already have Notepad++ with Spell-Checker plugin installed.

Download and Install the aspell full installer on http://aspell.net/win32/

Download and Install the desired dictionary (English for this example)

Test if aspell is working:

Open Command shell
type WIN + R then CMD on the input box

Go to aspell folder
> CD c:\program files\aspell\bin

Execute some aspell command
> aspell soundslike
> table

you should get
table TBL (TBL is the “sounds like” return of aspell)
Close the command shell

Do Notepad++ recognize aspell:

On Notepad++ installation dir, create the “aspell” folder and copy contents of installation folder on it. Your directory tree should be like that:

    Notepad++InstallFolder
      \aspell
      \bin
        aspell-15.dll
        aspell.exe
        pspell-15.dll
        word-list-compress.exe
      \data
        ASCII.dat
        dvorak.kbd
        en.dat
        en_phonet.dat
        iso8859-1.dat
        iso8859-10.dat
        iso8859-13.dat
        iso8859-14.dat
        iso8859-15.dat
        iso8859-2.dat
        iso8859-3.dat
        iso8859-4.dat
        iso8859-5.dat
        iso8859-6.dat
        iso8859-7.dat
        iso8859-8.dat
        iso8859-9.dat
        koi8-f.dat
        koi8-r.dat
        koi8-u.dat
        standard.kbd
        viscii.dat
      \dict
        american-w-accents.alias
        american.alias
        british-w-accents.alias
        british.alias
        canadian-w-accents.alias
        canadian.alias
        en-only.rws
        en.multi
        english.alias
        en_CA-only.rws
        en_CA-w-accents.multi
        en_CA.multi
        en_GB-only.rws
        en_GB-w-accents.multi
        en_GB.multi
        en_US-only.rws
        en_US-w-accents.multi
        en_US.multi  
      \plugins
        SpellChecker.dll
      \Config
        SpellChecker.ini

Edit the SpellChecker.ini file and change the path parameter to:
Relative Path=aspell\bin

Do NOT try to run the plugin yet!

UNINSTALL the original aspell otherwise the plugin will try reference it instead the Notepad++InstallFolder.

So..after everything done you should get everthing working

To install additional modules:

The tip: Use Winrar to extract files from .exe file.
After that, just copy the contents of \data and \dict folders and restart Notepad++