I own a business that is similar to UL. While it can seem daunting at first, it really isn't that hard to do. Using a level, make sure your design is straight. Then, using painter's tape, tape the top edge to make it sort of like a hinge. Then, flip the design up towards the ceiling, and peel the backing off. Do not try to peel the front off because it is just harder that way. I hope that makes sense. You might need a second pair of hands to help you hold it up while you peel off the backing. You don't want it to roll back and fold on itself (the back of the letters are very sticky). Once you have the backing off (I just let it fall to the floor), carefully roll it back down onto the wall, being careful that it is smooth without bubbles. Walls are very forgiving, so this step isn't too hard (if you are putting it on glass, you get one shot at it!). Then, use the application tool they sent you to rub it onto the wall, through the application tape. You can then start removing the application tape from the lettering. I find that with some walls, I have to use the application tool to sort of rub over the top layer as I pull the tape up. This helps the letters adhere to your wall. Move along at a 45 degree angle (from the corners up). For some reason that seems to be the easiest way to go. Just be mindful to watch the letters as you pull the tape up, that they are not sticking to the tape still. If they are, just rub that area a little bit more and try again. That is when I usually put pressure on the letters as I pull up the tape. Let me know if you need more help. I'm happy to walk you through it more.
Blessings!