I usually take a little bit of fondant (or gum paste if I already have that out) and bit it into little bits and drop it into some warm water. The fondant dissolves and helps make a gum, by making the water a bit stickier. Then I just brush the "petal gum" onto the back of the fondant piece and stick it on. I usually hold it there for a minute and you are done.
I just wet the back with a little water and stick them on. Not to much water because it will cause it to run .
I have always used vanilla. Just use a small brush and paint on a little vanilla on the back. Hold in place for a a few seconds and it should hold without any trouble. I have never had anything fall off. Just make sure you don't use too much or it will slide down the cake until it dries!
I do exactly what Marci does. I make it pretty sticky. and Not had any problems. If you are unsure, perhaps you can wait to attach them once you get where you are going, when you set up the cake? That way you wont have to worry about the transporting part. Just a thought.
I use a couple of methods to attach fondant accents:
1. just plain old water. Just make sure you don't use a lot or it will run (as someone mentioned earlier)
2. Piping gel is great to use for attaching things to fondant.