Shooting through glass

Pushing the lens right up against the glass, so the filter ring or hood is touching the glass, will prevent stray light (from your flash, for example) getting in and eliminate reflections. The problem with this is that you can only shoot at one angle - perpendicular to the glass.

Someone on this forum had the clever idea of using a rubber hood which would allow you to shoot at various angles but still keeping a tight seal against the glass.

Another possibility is a polarising filter, which might be your only option if the glass is out of reach.

Placing a bit of matte black card or translucent dark plastic in the right position against the glass, is a technique I have used successfully when shooting through windows. Often you can get away with just placing the card or plastic between the object being reflected and the glass, without having to push it against the glass. Choose an angle where you can both hold the card in the right place and get your shot, or take someone with you to hold the card. For obvious reasons this works best if you use a longer focal length, eg 55mm as opposed to 18mm on a standard kit lens.

A polariser could be an option as Tim suggests, but you might end up with light problems, unless the light in the museum is very good.

Thoughton's suggestions are very good - I'd also suggest picking subjects which have lights inside the case, and avoid standing between the glass and any external lights (i.e. windows & general room lights). Also pick clean bits of glass!

You probably won't be allowed to use Flash or a Tripod, so are unlikely to get shots anything like the official ones (they make much-needed money from selling these), so best to look for interesting angles and juxtopositions - shots like a transfixed child looking up at exhibit are priceless and often more interesting than just the exhibit...!