I know this is probably so simple and silly to some of you, but I've never had to "heat seal" a ribbon before. However I was working on a project today that included this as a step. So of course I had to look it up.
To heat seal a ribbon:
Simply hold the end of the ribbon tightly over a flame (candle, lighter, etc) and move from left to right once or twice.
(picture courtesy of http://needlesfabricandthread.blogspot.com)