How to hide fake green stems?

You could use stones/marbles/pebbles. I like when leaves are used. They also sell this ribbon that you can line the vases with: http://www.save-on-crafts.com/aspidistra-floral-ribbon-4-in-green-mangetsu.html

I like the stones/marbles/pebbles idea as well.

Depending on what your colors are you could use sliced fruit like lemons, lines, oranges etc around the glass. Google DIY sliced fruit centerpieces and they have tons of ideas and ways to do it.

Thanks y'all.