cluch?

how does a the cluch work on a manual trans, and how does it differ from a twin plate?

A twin plate is just a type of clutch that increases friction area by doubling the number of plates.

A clutch is like a brake rotor and a pad. The flywheel is spinning with the engine. As you let the clutch out, the other plate (attached to the transmission) covered in friction material begins to press against the flywheel. With the clutch the whole way out, there is no slippage.... if its working right :)

so when you let the cluch out and step on the gas the flywheel and cluch plate should be spinning at the same speed? if their working right that is

Once the clutch is fully out, yes. When its in, they aren't touching so they are independent of each other. The clutch would be not spinning at all if it was in neutral, or spinning with the wheels if its in gear.

When you are starting from a stop, the clutch is disengaged, which is why the engine can spin while the wheels are not. As you let it out, they start to connect with friction. Once its the whole way out, they are held together with enough pressure that they don't slip.