Many people hike "Y Mountain," but far more than that hike "the Y." Be careful not to confuse the two, as it is a 4 mile difference in round trip distance.
Hiking "the Y" means going up the first mile and a quarter of the trail to the big letter "Y" on the mountain.
Hiking "Y Mountain" means getting to the summit of the mountain. After getting to the top of the letter "Y" there is a small trail that heads South and up the mountain. That trail goes to the top.
When going to the top, the first mile (the part leading up to the letter) and last mile (that leads to the summit) of the ascent are the steepest parts. The middle mile still gains elevation, but not nearly as much as the other two miles. Use the first mile as a gauge for the trip, since it is of comparable difficulty to the top of the trail.
The middle mile of the trail is quite narrow, and it is easy to miss the fork in the trail that leads to the top. There is one fork marked by a tree with a "Y" carved into it. The left trail at the fork goes up to the summit, while the right leads to other forks for trails to Rock Canyon, Provo Peak, and other places. Again, it is very easy to miss this fork, but it is about a mile past the top of the letter "Y."
There do not seem to be any locations to get water on this trail, so do not plan on relying on a filter for your water.