Every pastel I sell goes out unframed. That is deliberate rather than a job left undone. Framing is where a pastel is most easily got wrong, and the choices are worth making deliberately rather than at a counter in a hurry.
Here is what matters, in the order it matters.
It must go under glass, and the glass must not touch it
Pastel is loose pigment held in the tooth of the paper. It is not sealed. Anything pressed against the surface will take some of it away, which means glass laid straight onto the painting is the one genuinely damaging thing you can do.
The fix is a spacer or a mat that lifts the glass a few millimetres clear. Any framer will know this, but say it out loud anyway, because a frame shop that mostly does photographs may not think of it.

That small gap does something else worth having. It gives the painting a little depth inside the frame, so the surface sits back rather than being pinned flat.
Glass or acrylic
Glass is heavier, cheaper and does not build a static charge. Acrylic is lighter and will not shatter, but it can hold static, and static will lift pigment off a pastel surface. If you have a choice, glass is the safer one here.
Museum or conservation glass costs more and cuts reflections and ultraviolet light. Whether that is worth it depends mostly on the wall.
Which brings us to the wall
Direct sunlight is the thing that will age any work on paper. Pigment is more lightfast than dye, so a pastel holds up better than many things, but the paper itself will warm and go brittle given enough years of sun.
Pick a wall that does not get a hard shaft of afternoon light across it. That is most of the advice. Normal room light, north-facing windows, lamps in the evening, none of that is a problem.
Do not spray it
Fixative is sold for pastel and I would leave it alone on a finished piece. It works by wetting the pigment slightly so it binds, and in doing that it darkens the colour and kills exactly the bare-pigment quality that makes pastel worth using in the first place. A painting under glass with a spacer does not need it.
Moving one
Flat, face up, with nothing resting on the surface. If it has to travel, a sheet of glassine laid over it and a rigid board underneath is enough. Never rolled.
Once it is framed, it is as robust as any other picture on your wall. It is only vulnerable in the gap between leaving here and going behind glass.
If you would rather not deal with any of this, prints are available for every piece and can be framed like an ordinary photograph. The full collection is in the gallery, and if you are wondering what makes the medium behave this way, I wrote about that in why I work in soft pastel.
— DawnE