I bought some Skin Bond to help them stick better. If you don't use it, they tend to fall off pretty quickly after a day or so.
I follow the directions on the Skin Bond, which is to apply a layer of adhesive to both surfaces - in this case, the ear and the strip - then let dry for 5 minutes (though I usually don't wait the full 5 mins).
Make sure you know the right place to stick it. When Suri doesn't have her ears erect, make a note of where the ear folds. You don't want to put the strip down past that or she will have trouble folding her ears back. I use the regular size Breathe Right strips (not the large), and just put one end at the tip of the ear and it never reaches down past the fold anyway, so you should be fine.
Then you just stick the strip onto the ear and adhesive and hold it there, making such it is completely stuck in place. And viola! you're done.
Watch for the ears leaning or looking too floppy. If this happens, you should continue posting.