My girlfriend's parents are visiting for a month - as a gentleman, how should I act/behave towards them?

I think gifts are more appropriate if you go to stay with them, and taking them out to a restaurant would be better in the first instance, especially if it is one typical of the country where you're both studying/working. I don't think you need do anything except be yourself, when you meet them. Say you've heard a lot about them and you're pleased to be able to meet them in person at last. Don't feel the need to make a speech about how much you love their daughter, let them see this for themselves in the way you look at each other. I think it's okay holding hands, when parents are around, but overt kissing and cuddling is maybe best kept for when you're both alone. Don't have too much to drink either. Hold the door open for the parents, always be well-groomed and just show that you're interested in them. I'm sure everything will go wonderfully. If you all get on very well and you want to buy them something, a nice souvenir of the country at the end of their visit will probably be appreciated a lot.