Firstly, you need to set your grill to a medium temperature. Cut your bagel in half and put the halves cut side in your grill. They need to stay in the grill until they turn crispy but not so much so they are brown.
While they are cooking, slice the cheese. Try to slice it as thinly as possible.
Take your bagel halves and butter them. Place your salmon evenly over one half of your bagel. Put your cheese on top of that, how much you put on depends on personal taste.
Put the bagels back into the oven. Leave them in the oven until the cheese starts to melt.
You need to have COOKED salmon for your bagel, NOT smoked. You can use leftover salmon from the fridge or you can cook some fresh. Put your salmon on a baking tray in an oven at 200 C / Gas 6 for 15-20 minutes.