Have you had a chance to read State and Revolution yet? Lenin was really helpful to me.
This is my (very) quick and possibly poor understanding. Please read State Rev to see if I misrepresent it!
-
"the state" is a machine for class oppression. At the current time, the bourgeoisie use that machine to oppress the proletariat, at one point kings used "the state" to oppress the nascent bourgeois class and peasants.
-
the machine of the state is the tools for oppression. The "special bodies of armed men" are necessary for the oppression.
-
the proletariat can take the tools away from the bourgeois, and create their own tools.
-
the proletariat can use their tools to "oppress". the bourgeoisie into being equal with them (and protect the revolution in the process).
-
once class distinctions have been oppressed into non-existence, the contradiction of class will be gone, and the people's police won't have anything to do.
-
after long enough without anything to do (100 years? Who knows?) the people's "state" (i.e. "special bodies of armed men") will "wither away". The people's police will go make steel or something useful.
The important things here are that we can't predict the future, and that it'd probably take the whole world being socialist before a transition into communism.
And that the state being gone doesn't necessarily preclude centralized administration - it's not oppression to coordinate trains and garbage pickup or whatever.
Tldr - read Lenin not me.