So you have to start from the scrap of paper, and glue it under the surface to be decorated not on it. That's why it's called decoupage UNDER glass.
Before proceeding with glue, it's better wash very well the glass surface very well with a washing-up liquid, in order to skim the surface, then dry it with a cloth which doesn't leave any hair. Now you can organize the figures of paper under the glass to see if you like the composition.
The figures of paper will be glued under the glass, and will be seen trough it, so it's necessary to glue it on the painted side. So instead of putting the glue on the white back of the scrap of paper, you must put the glue on the painted front of the scrap and set it with the painted and glued front toward the glass surface under the back of the object.
You can use vinyl glue watered down less than usual, or else the water varnish.
A good trick consist of spreading the glue under the glass rather than on the scrap of paper. Be carefull when spreading the glue not to create any air bubble, and use more glue than you normally do. I suggest to wet the scrap of paper, expecially when it's not cut out from specific decoupage paper, dry it with a paper napkin then stick the painted side under the glass that you have just spread with glue.
Now turn the object of glass (let's pretend it's a plate for example) and look for any air bubbles, because once the glue has dried they become quite evident. To get rid of them, let your fingers (covered with glue) slide from the center of the figure toward the side of it in order to push them out. Do not press too heavily or you will push out too much glue together with the air bubble, and there will appear another even bigger air bubble because of the eddying effect.
The scrap of paper, when seen trough the glass, should appear almost white because of the glue, then you will be almost sure that the coat of glue is enough to avoid all air bubbles. But if the scrap of paper appears trough the glass almost the same colour it would have when dried, then there is too little glue, and you can be quite sure there will appear an air bubble, and a big one. Unfortunately the air bubble is really ugly, as you can see on the red flower on the picture on the right:
Now you can clean a little the glass from the glue, in fact when it has dried it looks visible because looks opacque.
Using a wet and well squeezed paper napkin tap gently around the figure of paper you have just glued on in order to clean off the biggest drops of glue. Do not insist too much in this cleaning procedure because the glue has not yet dried, and you might damage the work.
Once the glue has perfectly dried, and the scrap of paper is still and fixed on the glass, then you can remove the film of glue that frames the scrap.
For this aim I use a wet cotton stick imbued with water and ammonia and I clean the glass around the figure. Using a paper napkin I dry the surface while proceeding.
Clean also the front of the plate of glass
If you use water varnish instead of glue, then you wuold work less, because you are not supposed to clean around the figure. Still I prefer the glue for its consistency. Normally I use the glue and clean as described above, if I want to paint the background, while I use the water varnish and I don't clean if I want to leave the glass transparent.
Make some attempts and see what you prefer.
Once the cleaning is over you can paint the background. I use acrylic enamel colours because they have a consistency I prefer when painting on this surface, but if you like you can use the normal acrylic colours too.
If you want to add some details, you must do it now before you paint the background. For example if you glued on a butterfly, then you should paint the antennas with a colour in contrast with the background. In this example I've painted the antennas white and the background black. You can also put your signature writing it the other way round.
Keep in mind that painting under glass is rather difficult especially the first times, You'd better not add too many details and choose one colour for the background because it's not so simple to control the result of shading.
Once the details have dried up, you can proceed with the background colour. You have to spread it all on the back surface of the glass object. Be carefull while giving the first coat of colour, because you might paint away the details you have just painted.
There will need two or three coats of painting if the colour is dark, more if the colour is light. The glass shouldn't be transparent any more.
Once the colour has perfectly dried up you can start varnishing. The decoupage decoration will be seen trough the glass, so you are varnishing the back of the object, and it's not necessary for you to give so many coats of varnish as you used to do when making classical decoupage, and it won't be necessary to use the abrasive paper either.
If you want a strong finishing you'd better use turpentine varnish, which is much more water resistant than a water varnish. The colour won't get yellowish, because the varnish is underneath, not on the top.
And here is the result: