OK, it goes something like this:

The clutch basket (#1) is firmly attached via a splined connection to the primary driven gear. Power is transmitted from the crankshaft here. The tabs on the friction plates mesh with this.
The clutch center (#3) is firmly attached to the transmission primary shaft. The tabs on the insides of the steel discs mesh with this.
The basket and center can turn independantly of each other.
Now, the lifter plate (#9) is connected to the pressure plate (#8) and these can move in and out relative to the clutch center. The clutch springs (#10) want to keep the lifter plate pressed outwards, which pulls outwards on the pressure plate, sandwiching the clutch discs between itself and the clutch center. In this state your clutch is engaged.
When you pull the clutch lever, the clutch lifter mechanism presses inwards on the lifter plate (#9) causing it and the pressure plate (#8) to move inwards. Meanwhile the clutch center (#3) stays where it is. As a result the pressure is released from the clutch plates and your clutch is disengaged.
The most common problem I've seen when reassembling these is to not have the pressure plate's inner splines properly aligned with the clutch center. Take just these two parts, and hold them together with no other parts involved. The studs on the pressure plate pass through the four holes in the clutch center. When they're together, notice the outer splines on the clutch center - they should align with the similar splines on the face of the pressure plate (not visible in picture). Only one orientation will work - try turning the plate 90 degrees at a time until the splines line up properly, then mark the parts with a sharpie so that you can align them that way when you reassemble everything.
When the splines do not align properly, the clutch plates won't slide all the way down into the pressure plate like they should. As a result, the clutch pack is too wide and when you tighten down the spring bolts everything locks up and won't move. The pressure plate is already being forced inwards by the splines on the first steel plate, so it can't move any further, but because the splines are pressing against each other the clutch is 'engaged'.
hth
mystic_1
Edit: In other words, what 754 said! lol
