The Egyptian government has taken a variety of steps to make it as safe as possible for visiting tourists. In many ways it is far safer than many other countries, though when travelling ANYWHERE you should always be on your guard - don't wear obvious jewelry, wave a lot of cash around, or wander off entirely on your own without letting someone know where you are going.
As far a risks of terrorism, yes there have been incidents in the past and there are still some extremist groups operating in Egypt. However, the vast majority of Egyptians do not think that murdering people is the right way to go about making changes in the world, no matter what their politics and they also realize that much of the nation's income comes from tourism.
Nearly everyone I come into contact with in various parts of the country is welcoming, friendly, and perfectly able to distinguish a person of a certain nationality from that nation's policies.
So long as you are equally friendly, polite, and respectful of the country in which you are a guest you should have no problems.
With that in mind, I strongly recommend you purchase and read a recently published travel guide to Egypt - any of them should do.
Avoid wearing shorts or sleeveless shirts whether you are male or female unless you intend to remain within the grounds of a hotel. Any number of tourists do this and most Egyptians in the tourist-heavy areas seem not to mind, but frankly it's rude - it's considered to be a display of too much skin and honestly you are better off in long pants and at least short sleeves for protection from the elements. If you intend to visit historic mosques, follow the rules posted and don't bother those there to worship.
In essence, be polite and open minded and you should be fine.