It doesn't really pay to even download it from the App Store. The new design is a terrible change from the one that used to be on the home screen. It's harder to navigate and it's so slow, unrelated to how good your Internet connection is. It's better to visit their website trough Safari, which even that isn't so great, but better than the app.
go onto safari and on youtube.com and click one of the buttons on the bottom of the screen ( sorry to be so vague but i just switched from apple phones to droid so i dont exactly remember everything ) and it says something like save to home page as one of the options. click that and then u will have a youtube app. hope this helps (: