I play a song in standard tuning on the guitar. The song requires a 'G' harmonica. I tune the guitar down to D-G-C-F-A-D. What key of harmonica would I need for the same song in this tuning?
Although it seems straight forward and simple, this is actually a tricky question.
The tuning you describe is simply standard tuning - except one whole step flat. Everything Bob Broadley said in his answer is theoretically correct with one minor glitch (for G to F) created by the harmonica makers.
In the example you used for your guitar tuning, if you order a "regular/standard" F harmonica (thinking it will be like your G harmonica only one step lower), you may be in for a surprise!
A typical F harmonica in the standard diatonic configuration and tuning will actually play almost an octave higher than a standard G harmonica. With most harmonica makers, the G Harp will be the lowest tuning - and A, B, C etc. all the way through F will all be higher in pitch. Until you get outside of standard and typical harmonica tunings, G will be the lowest key and F will be the highest.
I am assuming that by tuning a full step flat, your intention is to sing a full step lower. If that is in fact the case, you will need to order a harmonica in the key of "Low F" to provide the same relationship to your guitar tuning as a standard G harp would if your guitar was tuned standard - and you were playing a song that would normally be played with a G harp.
Of course you can still use the higher pitched standard F harmonica, just be aware that what you are playing on your harmonica, will be an octave higher than what you are playing on your guitar (as compared to using a G harp with standard tuning).
Below are a few other important points for general reference to help aspiring harmonica players who come across this information in the future.
A standard typical diatonic ten hole harmonica ("harp") such as Hohner Special 20 or Hohner Marine Band Crossover, or Lee Oskar Blues Harp, is tuned in what is known as "Richter Tuning" and will have the same relative note layout in each key. By relative note layout, I mean once you learn to play a tune on a harp in a certain key, you can easily play it in other keys on any other key harp (ten hole diatonic), using the same holes and pattern.
It may also be helpful for beginning harmonica players to understand that determining which key harmonica to use for a particular song - is not always intuitive and simple. For example, when playing Blues - most harmonica players will play what is known as "cross harp" and bend many of the draw notes to give the harmonica a more bluesy sound. So if you want to play a simple melody like "Twinkle Twinkle Little Star" in the key of G, you need a harmonica in the key of G. However, if you want to play blues in the key of G, you need a harmonica in the key of C to play "cross harp".
There are also harmonicas that are made in tunings other than the Richter Tuning - such as Natural Minor, Harmonic Minor and Melody Maker to name a few.
Adding harmonica to your musical arrangements is fun and fulfilling and adds a new dimension to the music. Enjoy the process of learning to play more songs on harmonica and best of luck to you.
Standard tuning on the guitar is E A D G B E, from the lowest/thickest string (6) to the highest/thinnest (1). Therefore, tuning the guitar strings down to D G C F A D, from lowest to highest, will make them each exactly a whole-tone lower (the same as two semitones, or two frets, if you like).
Therefore, playing the music on your detuned guitar, in the same way as you did with standard tuning, everything will now sound a whole-tone lower.
So, if a G harmonica was suitable for playing this song with a guitar in standard tuning, you now need to use a harmonica pitched a whole-tone lower. A whole-tone lower than G is F.
Use an F harmonica.