It is not as steep as, Half DOme. Of course, it is uphill :-) But the main difficulties are the distance and the altitude: it is a full day of hiking and it is mostly hiking at altitude, which makes everything much more difficult.
Most people don't go to the top. Most people stop at the first lake, or at the second lake. Nature is pretty impressive, so I don't think you will disappointed even if you do only 1/4th of the hike.
The regular trail has only one fork and it comes almost at the end. Needless to say, you have to go up, so turn right. There is another trail, but it is difficult to find it even when you want to, so I wouldn't worry about it.
The other trail is called "North Fork trail" or the "mountaineering trail". It is a lot steeper (ten times steeper) than the regular trail. Going up is absolute hell. So very few people use it. The good news is that nature is ten times more impressive along this trail than along the regular trail. So if you already know that you are not going to the top and you are not afraid of heights, you may want to hike this "North Fork trail" till the second lake (no relationship to the lakes of the regular trail). (The North Fork trail does not require a permit: if you are worried about rangers turning you away, then you should hike the North Fork trail).
Downhill it takes seven hours for almost everybody. Uphill depends: seven to ten hours. To be safe, we leave at 2-3am. That's why we always pick a full-moon weekend.
This area is rich in tourist attractions. The town that we use as a base is Lone Pine. From Lone Pine you are about 2 hours from Eureka Sand Dunes, the tallest dunes in northern America. It is part of Death Valley park but they can only be reached from the north, so very few tourists visit them. If you have a 4x4, there are many other things you can do around there. Also, don't forget that getting to Lone Pine implies crossing the whole of Yosemite Park, passing by Mono Lake and by the Mammoth Lakes. Devil's Postpile national monument is also along the way. The highway that goes through Lone Pine, highway 395, is considered one of the most interesting in California. Right in Lone Pine, the Alabama Hills (which are really rocks in the desert) have been the site of many Hollywood films.
As I said, there is plenty to do in the area. Every year we have somebody who does not hike and prefers to do sightseeing.
Driving from the Bay Area to Lone Pine takes at least seven hours. So the minimum you should consider is two days. Best is if you can take friday afternoon off and monday morning off. In that case: you drive to Lone Pine on friday; you spend saturday acclimatizing and visiting nearby attractions; you hike sunday; you drive back sunday evening; you rest monday morning. If you hike to the top, you will be very tired (and sleepy) on monday morning. Also, don't forget the main problem is the altitude: if you just drive there and start hiking, you will suffer altitude at its worst. Much better to spend one full day in the area and get used to altitude. Mt Whitney is 4400 meters tall. The campground where we usually camp is 2800 meters tall. Even if you spend one day at 2800 meters, you will still feel the altitude while you are hiking. Imagine if you don't even spend a day there. Also, if you get to Lone Pine on friday night, you can go to the rangers station on saturday morning and get a permit for the hike.