The First Crusade is an unusually well-documented event so fortunately we know lots of specific dates. However, if you mean how long did it take everyone to sail there, then they didn't - almost the entire crusade was overland and everyone walked from Europe to Jerusalem.
November 27, 1095 is traditionally considered the starting point, since that's when Pope Urban II gave his speech at the Council of Clermont. The departure date was set for August 15, 1096.
Before that date, some relatively unorganized groups of crusaders set off by themselves in the spring and summer of 1096. The first thing they did was to attack the Jewish communities in the cities along the Rhine and elsewhere - the largest attack was on May 18 when hundreds of Jews were massacred in Worms.
These roving bands of crusaders were not the kind of professional knights that Urban had hoped to recruit, but they eventually sort of got their act together, and reached Constantinople on August 1 - still two weeks before Urban's "proper" crusade army was supposed to leave. They crossed over into Anatolia but by October almost all of them had been killed in various battles with the Turks.
The armies recruited by Urban left from various places in France and Italy at the appointed time in August 1096. They took different routes and they all ended up in Constantinople between November 1096 and February 1097. They crossed into Anatolia as well and besieged Nicaea in May and June, 1097, and in July they defeated the Turks at Dorylaeum.
Then they took their time crossing Anatolia. Most of them headed for Antioch, where they arrived on October 21, 1097. They defeated the Turks there on June 28, 1098 (921 years ago today if it's still June 28 when you're reading this!).
They didn't continue south to Jerusalem until January 1099. It took another six months to get there: they arrived on June 7, and Jerusalem was captured on July 15.
The capture of Jerusalem is one possible stopping point for dating the First Crusade, but another typical date is August 12, when the crusaders defeated the Egyptian army that came to try to recover Jerusalem.
A few crusaders did go by boat. Some of them crossed from Italy into the Balkans by boat, but that was just to get to Constantinople. They had to cross the Bosporus by boat, from Constantinople into Anatolia. A fleet of English ships arrived to help out with the Siege of Antioch, and a Genoese fleet brought supplies for the Siege of Jerusalem in June 1099. The Genoese didn't participate directly in the siege though, since Jerusalem isn't on the coast.
Later crusades often did go by boat because there were friendly crusader-held ports where they could land safely, but those weren't available yet before the First Crusade was over. Assuming they could have landed somewhere during the First Crusade, the journey by sea typically took 5 weeks or so.
But since this crusade largely did not travel by sea, the answer to your question is November 27, 1095 (initial call) to June 7, 1099 (when they arrived at Jerusalem), or July 15, 1099 (when they captured Jerusalem), or August 12, 1099 (when they won the Battle of Ascalon).
For a basic history of the First Crusade, including a very helpful chronology at the end, see Thomas Asbridge, The First Crusade: A New History (Oxford University Pres, 2004), pg. 342-344.