This is easiest if you get on Yoshi (although it's still somewhat difficult). Go to where you enter Delfino Plaza in the beginning (by the statue). Now, turn around and go to the left edge of the building to the left of the water fountain (see screenshot). Now, spin jump if on Yoshi (rotate the control stick and A) and try to hit the close edge of the roof. If you're not on Yoshi, you'll have to do a combination of triple jumps, wall kicks, and hovering. You want to just barely land on the edge of the roof, so that you go through it. This will take several tries.
Once you're below Delfino Plaza, there are a couple of things you need to worry about. First of all, JUMP! Repeatedly. If you stay on the ground for a couple of seconds, then you'll spontaneously die. Weird. Also, beware of the underground tunnels that lead into the manholes. If you run into one while exploring, then you'll go into it and end up in a normal non-glitchy area. You can go to lots of cool places with this glitch. If you can make it to the water, then you'll be able to walk underwater. Yoshi can do it too... but if you jump too high, you'll land on the water and Yoshi will die. This is useful for bringing Yoshi to that pipe in island in the middle of the water.
Submitted by: CyberGlitch