Getting there is half the fun. Timbuktu did not earn its reputation for being at the end of the world for nothing. You have three options: air, road, and river.
By air
There are flights from Bamako and from Mopti. Schedules change frequently, so confirm before you plan around them. A bus runs from the airport to town for about 1,000 CFA.
By road
Not easy, but possible in the dry season. You can get here by 4WD or by bus from Bamako via Segou -- count on at least two hard days of driving. In the wet season the roads become impassable, and a boat is the better option.
By boat
The most scenic and most memorable way to arrive. Riverboats run from Mopti (about three days) and from Gao (three to four days), with stops at villages along the way. You will see good birdlife and, on the Gao route, possibly hippos. Chartering a pinasse from Mopti costs around 300,000 CFA and technically seats twenty, though more than six people will be cramped. The boat docks at Kabara, about ten kilometers from town.