There are a lot of ways to do ascend Mt. San Jacinto. A common way is to do it from the tram.
Here's a map link that you can use for driving directions:
http://maps.google.com/maps?f=q&hl=en&geocode=&q=1+Tramway+Rd,+Palm+Springs,+CA&sll=37.0625,-95.677068&sspn=52.107327,77.519531&ie=UTF8&t=h&z=17. First tram is at 8:00 AM on weekends (and holidays I think) and 10:00 AM on weekdays. It costs about $25.00. There is a AAA discount if you've got an AAA card.
Here's a topo map of the area:
http://www.parks.ca.gov/pages/636/files/MtSanJacintoSPmap.pdf. You want to go from the Mountain Station of the tram to the Ranger Station (which is just west of the tram after you descend the long concrete exit ramp) to get your day hike permit. Better call ahead if you want an overnight permit. From the Ranger Station, go to Round Valley. From Round Valley go to Wellman Divide. From Wellman Divide go to the trail junction just south of the peak of Mt. San Jacinto. From the trail junction, go north to the peak. A portion of the final section to the peak does not have a trail; you're just scrambling (class 2) over rock. Many people have a hard time in this section and can't find the trail on their way back. It's probably best to bring a map and compass and to stay oriented the whole time. From the peak, return the way you came. Don't forget to hold onto your ticket stub. Sometimes they check on the way down.
If you don't like the tram idea, check out that topo map link. There's at least half a dozen different ways to climb San Jacinto.
There you have it.
HJ