I've been there! Currently, I am making a show, but it's not on YouTube. So, let's start from the beginning!
How to make an intro: I would get the app Video Star. The app doesn't cost any money, and you can use it! Some of the REALLY cool effects cost money, but you can still do effects without paying a dime, or, yeah, a penny or whatever. XD.
How to put your clips together: I would get the App Movie Maker. Again, it doesn't cost anything. The only down-side is that you can only put in two clips at a time. It'll take longer, but you're not costing anything.