This trope has been used lots, but that doesn't necessarily mean that there are no new ways to approach it. There are thousands of iterations of the same stories, but they're each different and engaging because they tell their own tales in their own way.
In order to make your story feel fresh, you just have to do something different with it, whether that is done with plot, setting, magic, characters, or something else. Worldbuilding.SE is a great place to start off with trying to come up with new ideas and angles.
You could start off with the character accidentally being summoned into another world that was trying to conjure a powerful demon, and got the spell mixed up and summoned a random person instead. You can have someone introduce technology into a fantasy world by accident, setting off a battle between technology and magic.
As for integrating the character, you can approach that in any way you want as well. Perhaps they are transported to a world where the people look like humans, but the MC is actually much stronger than most people in that world, despite being average in our world, giving them a physiological advantage over others whilst they learn about how to survive in a fantasy world they are not yet accustomed to. Incorporate their unfamiliarity with the new world into their character growth, as they develop their understanding of this new world, so do they develop as a person.
As for something necessary for the character, I would say they would definitely need to have an opinion on returning to their own world. Whether they love the new place, hate it, or have mixed feelings, they would not suddenly forget about it.