It varies depending on the writer, but the fastest person in the DC Multiverse is typically the Flash (whichever version is most prominent at the time).
Commonly there are foot races shown between Flash and Superman, with it almost always resulting in a tie.
Flash addressed this directly when he was once seeking some alone time and Superman was trying to talk to him. Superman easily caught up to Flash and said, "Barry, come on. We've raced before and you know I'm just as fast as you." Barry responded with, "Those races were for charity, Clark" and sped away.
At different times, each version of the Flash has been faster than the rest. Sometimes it's because of training, sometimes because of a better understanding of (or compatibility with) the Speed Force, sometimes it's just because they need to be faster.
The Flash is the fastest man alive...but which Flash currently bears that title differs.