sunshinegal speaks about the reasons for Tisha B'Av. Here, I'll talk about the practises.
As mentioned above, Tisha B'Av is the saddest day in the Jewish year and is most well known for being a fast day. Orthodox (and other committed) Jews fast for 25 hours - and fasting for Jews means not eating or drinking anything. As with other Jewish fast days, minors (girls under 12 and boys under 13) don't have to fast, although as they get older they may want to. Due to the sadness of the day, they should be encouraged to refrain from doing anything too exciting, and should only eat basic food. If fasting would be dangerous to your health (eg if you're diabetic, elderly, or have just given birth], it is forbidden to fast, although you should consume the minimum required to keep yourself going.
The fast runs from shortly before nightfall on the previous evening, until shortly after nightfall on the day itself (Jewish days run from nightfall to nightfall). There is one other 25 hour fast in Judaism - Yom Kippur. However, this is very different as although it's the holiest day in the year, it's not a sad day as such.
It is important to eat, and even more important to drink, enough before the fast starts. However, in line with the restrictions on the "Nine Days" running up to Tisha B'Av, meat isn't consumed. Many have a tradition of eating a hard-boiled egg, or a piece of bread, dipped in ashes, as the last thing before the fast starts, to commemorate the destruction of the Temple.
At the start of the fast, leather shoes are removed and canvas shoes (or other shoes not made from animal skin) are worn. The Synagogue is set in a subdued manner - the lights are dimmed and the decorative covers on the Aron HaKodesh and the Bimah are removed. People sit on low chairs or on the floor, a Jewish sign of mourning - the same as is done when Sitting Shiva. The evening service is held in the Synagogue. This starts out like the regular weekday evening service. Afterwards, the book of Lamentations / Eichah, written by the Prophet Jeremiah is read. This talks about the destruction of Jerusalem. It is usually read by the Rabbi and/or members of the congregation in a slow, haunting melody. After this, a few Kinot are recited. These are best described as poems that have been written over the years describing the destruction of the Temple. The evening service then finishes as normal.
The Shacharit (morning service) is read in the same manner, with all the prayers said slowly and quietly. The Tallit, usually worn at every morning service by married men, isn't worn on Tisha B'Av at this time. Neither are Tefillin. A few sections of the prayers which are considered happy are also missed out. At the end of the service, Kinot are read again - this time, many more of them covering the things that have befallen the Jews over the years from Temple times, throughout the Middle Ages, and in most commuinities, finishing with a Kinah about the Holocaust.
Tisha B'Av doesn't have the same level of holiness as the festivals, and therefore, one is permitted to go to work. However, it's seen as better not to in the morning, if possible. And, of course, many people would rather not work at all if they are fasting.
The Afternoon service is the same as the afternoon service for any fast day, including Kriat HaTorah and a Haftarah. The Tallit and Tefillin are worn to make up for not wearing them in the morning. As it is usual to finish the afternoon service about one hour before the fast is finished, many Synagogues will show an appropriate film before the end of the fast. This would be something appropriate to the day - perhaps a documentary on the holocaust or on Jewish history.
When the fast finishes, one can eat and drink immediately.
Like all the fasts except for Yom Kippur, Shabbat takes precedence and we don't fast on Shabbat. Therefore, if Tisha B'Av falls on Shabbat, it is postponed until the Sunday.
When Tisha B'Av is on Sunday (either because that's when it fell, or because it's been postponed from Shabbat), the procedures are changed slightly. This is because any form of "public mourning" is prohibited on Shabbat. One would still eat a large meal late in the day, before the fast starts (which is about one hour before Shabbat finishes). However, the egg dipped in ashes isn't eaten. One must wear their Shabbat-appropriate shoes to Synagogue, and, having left canvas shoes there before Shabbat, change into them at the start of the evening service. Havdallah isn't recited on the Saturday night, but is instead postponed and recited after the fast finishes on Sunday evening.