Why does my clutch engage/disengage very close to the floor?

For those owning a new clutch, it is normal for the engagement point to drop low. The DSM clutch mechanisms are so constructed as to move the engagement point higher as the clutch wears.

Jack's how to adjust the clutch

Next try Jafromobile - Bleed your clutch.

Gary Selph, John Snodgrass and Kevin Fabec all found one of the connecting rods for the clutch mechanism was worn, causing the clutch to engage lower that it should. This may be a fairly common but easily overlooked problem, especially on older cars. A good test is to see if you can pull the clutch pedal up with your foot. If you can, the rod is likely worn.

Another commonly overlooked clutch problem is wear on the clutch fork or pivot ball. The clutch fork could also possibly be bent, especially if heavy-duty clutches have been used. The pivot ball and clutch fork have both been mentioned as 'wear items' and should be considered for replacement if a new clutch is going in anyway. 

See Jack's Pivot Ball Shimming: 

Of course, the problem may also be related to the clutch master cylinder. Replacing the cylinder and clutch lines can sometimes fix the problem. A few people have used stainless steel lines. It is far from required, but some people have found a steel line improved the clutch pedal feel quite a bit.