Tioga Pass is the only Yosemite entrance on the eastern side of the Park.  Tioga Road / Highway 120 is a beautiful drive, but it helps to be prepared. 

This scenic drive demands concentration due to the tight bends and drop offs, but it has stunning scenery that makes it worthwhile.  The secret is to take your time and to use the turn outs often; never feel pressured by vehicles behind you to drive faster than your comfort level.  Much of the road is through the forest and there is always some space at the side of the road.  But it is a mountainous drive with lots of curves.

For some eastbound drivers, the worst bit can be the final descent as you exit the park and travel the pass down to Lee Vining.  Driving close to an edge that drops off sharply around 2000 feet isn't what most drivers are used to, so it can be challenging.  Check the views on Google Maps for specifics.  

Traveling westbound and heading up the pass is less demanding as you will be traveling on the inside lane.

Tioga Pass is typically closed from November through May, but check the Yosemite NPS website for specific opening and closing dates.  Historical Tioga Road Opening & Closing Dates

Here is someone's timelapse movie of their Tioga Road drive from Crane Flat to Tioga Pass on June 23, 2011.  MOVIE