To get to the Citadel it is best to take a taxi. Just get in and say "Al-Qalaa." It should be no more than 6 LE from downtown. The main enterance is on Sharia' Salah Salem, and it will cost you 20 LE, or 10 LE for students, to get in. Beware, the Citadel closes at 5:00 and if you want to see everything, expect to spend 2.5-3 hours.
When you enter you will be in the Southern Enclosure and will pass a few, mostly pointless shops. Immediately follow the signs to the Muhammad Ali mosque. Love it or hate it, most hate it.
The Muhammad Ali mosque towers on top of the Citadel and is impressive in size. It was modeled after the Ottoman mosques, however the inside looks like a cheap attempt to build a "modern" mosque resembling the Dolmabahçe Palace in Istanbul. Nonetheless, it is quite the site, and worth seeing. Even more impressive are the views from the top of the Citadel. You can see all of Cairo, even the Pyramids, depending on how hazy it is.
Also worth seeing in the Southern Enclosure are the Mosque of An-Nasir Muhammad, and the Gawhara Palace. The An-Nasir mosque is a nice Mamluke mosque and the Gawhara is the palace of Muhammad Ali. There is also a nice Police Museum. There is also a nice Sufi dancing show in the Southern Enclosure on Sat, Mon, and Wed nights (see my journal on Sufi dancing).
After the Southern Enclosure, head up to the Northern Enclosure and the Military museum. The military museum offers a nice collection of artifacts from Egypt's Pharonic, Mamluke, and Ottoman pasts, as well as the present. If you do not know too much about Egyptian history you might be lost in some parts, but it is a nice museum worth seeing. Note though, that you have to pay to use cameras, so don't bother taking pictures.
Also in the Northern Enclosure is an interesting Carriage Museum, an Antiquities museum (although it's all in Arabic) and the very nice Mosque of Suleyman Pasha.
That about does it for the Citadel, but if it is still early and you aren't tired yet, I suggest walking back around to the bottom of the Citadel and checking out the Mosque and Madrassa of Hassan Pasha. A massive construction built in the 14th century. There is also the impressive Mosque of Ar-Rifai, which houses the remains of such notables as the Shah of Iran and King Farouk, and if you give a little "baksheesh" (tip) you can see the tombs.