I love this melody so much more than the typical tune to "Come Holy Ghost" that we sing at mass. I normally love those traditional anthems in 4/4 time, but the traditional Gregorian chant melody expresses the more mysterious and gentle action of the Holy Spirit. This melody makes me think more of the wind, and more of breath, more of sanctifying grace, than the far less subtle "Come Holy Ghost" tune from the missalette.
There are many fine renditions of Veni, Creator on YouTube, and I urge you to listen to a bunch of them. But I'm sharing this one because it's an average guy with an average voice, singing in a non-church setting. In fact, it looks like he's singing it with his breviary in his hands. I think a lot of people avoid trying to sing Gregorian chant because we usually hear it sung by scholas or choirs of well-trained singers in an acoustically perfect cathedral. We think, "Isn't that beautiful!" and "I can't sing like that." Well, you can sing like this guy: by yourself in a normal voice in a normal house and you will still be offering a priceless little jewel of praise to the Holy Spirit.
If you listen to this enough you will pick up the tune, and then be able to either sing it in Latin OR apply the same tune to most English versions of the lyrics.