How do I let this guy know that I like him without saying it?

Well first of all it may be a good way for you to get over some...or rather it just gets your mind off of them. But as for the guy your getting with, he ends up a rebound and he gets hurt in the end is the scenario. I hope it's not the case and you do really like this guy and don't only want to be with him just to get over another guy. *from experience it doesn't work, and friends of mine too* Your feelings for the other guy just become hidden.
You have to justify your reasons on WHY you are better than to just pine after that guy. YOU have to make yourself happy. And personally I think the best meds for that are truly good friends. And ice cream =P Only if you can eat when your depressed over a guy.
What your friend said is just a stereotypical solution, a thought only to make you feel better for time being. And people may think it works for a short period but someone always ends up getting crushed.

Rebounding is possibly one of the worst ways to try and get over someone else. Until you have gotten over the first guy, do not look for a new person yet. Go out, hang with your friends, eat good food, enjoy life, and most importantly remind yourself that guys are most definitely NOT the most important thing in the world.
Right now all you need to do is figure out how wonderful and beautiful and compassionate YOU are and that you don't need other people to validate your existence. Good luck, I know it isn't easy.