The first step in repairing damaged stainless trim is to determine what kind of dent you have. If it's a sharp crease, sharp ding, or just a more gentle crease/ding. The appropriate reverse force needs to be used on the back side of the trim. Clean the back side of the trim so that you can easily see the damage. Make sure there are no pieces of dirt lying around to cause more damage as you pick out the original dent. I have an assortment of blunted screwdrivers, chisels and punches that I've collected and ground for this work. Be careful that all edges of the tool that contact the trim are radiused. Any sharp edge will cause more damage. If it's a sharp dent, it will likely need a little mechanical force to be removed. If any factory crease lines were lost in the damage, you can reform them as you remove the dent. I would lay the trim face down on a smooth wooden or plastic surface (not metal)and very gently pick at the backside of the deepest part of the dent working the entire area a little at a time. Don't completely raise one section then move to another. Gradually work the whole area a little bit at a time removing the deepest sections first. Once the deepest section has been pushed out to about the level of the surrounding dent, work on that whole area next to bring it up. The idea is to get the whole damaged section back to original shape at the same time. If you completely remove one small section of the dent and them move to the next, you'll stretch the metal and have a hard time getting it flat. This also is the reason not to use a metal surface to work on.
Keep hammering confined to the sharp creases/dents only. After you've worked out the sharp crease/dent portion, try to push the surrounding low area out with a blunted tool. I have some screwrivers with nicely round handles that I use upside-down just for this. Put it on the spot you want to work and lean on it a bit. Be careful that there's no dirt between the tool and the trim or the work surface and the trim as it will dimple the stainless. You'll be surprised at how soft this metal actually is. After picking/pressing out damage, either use a very fine file or a sanding block with 360 grit or so to find the high/low spots on the front side of the trim. This will tell you what spots you may have to push up and which to push down to get the metal flat. Be very careful how much you sand and what kind of file you use since all these scartches will have to be polished out. I'll usually mask off the nearby good parts of the trim so I don't mar the finish as I'm working. If there were any gouges in the trim, those will have to be picked so that they are a little high and then sanded off. This is the trickiest part. That metal's thin and can be sanded through. Be careful. One piece of advice here: a file makes the flattest surface, but will cut through quicker. The sanding block (small wood block with sandpaper wrapped around) doesn't cut as aggressively, but won't get the surface as true. I'll usually use both to some extent. It's really easy to scratch the surrounding trim with the file so I'll tape the very end of it to eliminate this.
After you think you have all the damage out, wet-sand the area with 600 grit, then 1200 to get out all sandscratches. This takes time but you'll really see the sheen with the 1200. Lastly is polishing. I have a 3" polishing wheel and compound sticks that I bought from Eastwoods that has a collet on it designed for a drill. I put this in my multi-speed mini drill press and set the speed high. Once again I'll tape up any sharp surfaces on the nearby press. It's really disheartening to be almost done and slip off to hit the chuck and put a row of scratches right across all that hard work! (been there) Put safety glasses on, pay attention to which way the polisher spins so it won't bite the end of the trim, and move fast with the metal while pressing very lightly. If you dwell in one area trying to polish out scratches from the earlier steps, you can burn and warp the metal.