Mount Sinai is said the be the historical mountain where Moses was spoken to by God in the form of a burning bush. It is held in high regard by Jews, Christians, and Muslims, so please be repectful as you climb.
The climb up the mountain is far different from the climb Moses made thousands of years ago to be sure. Today there is a nice wide camel path that will guide you gradually up the mountain. Along the way are throngs of camel sellers, as well as four or five stands selling water, soft drinks and candy. It's not likely that Moses stopped for a Snickers on his way up but, whatever, the climb still offers spectacular views.
During the summer I suggest not going up during the day; the heat is absolutely unbearable and dangerous. Plus, seeing the sunrise from the top is a magical experience. If you leave around 2:30-3:00am you will make it up in time for sunrise, but bring a flashlight and warm clothes. It gets cold on top of the mountain. Blankets are also for sale on top for about 5 Pounds.
There are 2 ways up the mountain, the Camel Trail and the Stairs of Repentance. For all but the most fit and adventurous, I suggest the Camel Trail; it will take you the majority of the way up the mountain, but you still will have to master one last set of stairs. The Stairs of Repentance are 3750 steps built by a monk for repentance. They go straight up the 2285 meter mountain and it will likely leave you breatheless by the end. If you are going to do the stairs bring lots of water and be very careful at night. I suggest for the average hikers around to go up the camel trail then come down the stairs. Coming down the stairs is not too difficult and it offers great views of the monastary.
On the top of Mt. Sinai there is a Greek Orthodox church as well as a mosque, although both are usually closed. During the summer months the mountain is often flooded with people waiting for the sunrise and fighting for spots on the mountain. I found that if you get up the mountain aroun 4:30-5:00 you should beat the rush and get the best seats, to the right of the church on the ledge. Then all you have to do is snuggle up with your partner, or chat with your mates and wait for the sunrise. You won't be disappointed.