I made my logo in illustrator and the intro with with After Effects.
But how it's made isn't really important as it could be as simple as an image and music. The most important thing about an intro is it's length, try and make it as short as possible.
Mine is about 2 or 3 seconds long which I think is the sweet spot. I've seen so many videos where the intro is 15 seconds or more, by that point most people lose interest.
A lot of youtubers don't recommend having an intro but if it's incorporated well it can be quite effective.
Beastby