Sebastian, were are you located? I am living in Hamburg. If you happen to live in the area, maybe we might meet and I show you how to "blues-harp".
The others are right: for acompanying a folk song "Wandervogel-style" you need the same tuning as the song. For this kind of folk play you could even think of using a tremolo harmonica.
Using a harp this way gives a very sweet and pleasing sound. But if you want to pepper up the song a little bit, playing a blues harp cross chord is the thing to do with folk and country. It is not so difficult as it seems. And I must admit, what I read in the net is not very easy to understand.
For a beginning you should start playing a song in G on your G-harmonica. Concentrate just on one thing: allways play just one tone at a time. You achieve this by 1. blocking the other holes with your tongue or 2. closing your mouth until only one hole is open to the stream of air. Method 1 is recommended in the books, but method 2 is much easier and does it as well.
When you are a little comfortable with your mouth-harp, and you have a feeling which tones are played by sucking and which are played by blowing into the holes, you should try to play a chord in D. The blown D is located on the 3rd cancella (the correct name for the holes), counted from left (low tones) to right (high tones). You will recognice that there is also a D when you suck the 2nd cancella!
Now start with the blown D on the 3rd cancella, suck the same hole and move upwards hole for hole while first blowing then sucking each hole. End it when you reach the D again, now blown on the 6th cancella.
What you listened to is the blues-scala. You will have recogniced that there are tones from the major key scala missing. Instead there are very sharp tones in between which shouldn`t be there...
If you try to accompany a song with this scala, you will find out that there are gaps. You will not be able to play every tone from the melody. Expecially the E (second in the D major scale) will be missing quite often. Never mind! You can force your mouth harp to fill in this gap! Play the 3rd tone (the fis), you must suck the 3rd cancella for this. While you do this try to FORCE the tone to climb down! Move your harp a little against the lower lip, and try to suck the air a lot sharper than before. You will reach F (from the minor key) very soon, and you even can go down to the E with a little practice.
Everytime you want to play E, use the down-forced Fis. Try it with other melody gaps as well. Soon you will get the feeling for this distinctive "blues harp" sound!
Just a warning: Treating your harp the blues way instead of "wandervogel"-style is like kicking and scratching and shouting animal names while having sex. Treat your harp like a woman: use your hands and your breath to gently warm it up before you get to the hard and heavy parts of the story. If you leave her cold she soon will be nasty to you and loose tuning before time.

I could have written this in german but with respect to the international character of the mudcat forum I stick to english. If you need advice in german mail to thorkel@bigfoot.de and I will try to help you further.