Power Everything

How do you rewire a lamp? Everything from the power cord to bulb housing.?

I took apart the lamp (it's really tall) and all I wanted was the cord and bulb housing to mount it to something else. When I tried rewiring it and turned on the power it shorted out everthing in my room. Now the switch will not turn.

What you probably did was not connect the wires to the socket correctly. The bulb socket has a hot and neutral. The hot will be brass colored and the neutral will be nickel colored or brass with some black marker color on it. Your cord, if it is polarized( one prong fatter than the other) is hot and neutral sensitive. The fatter prong is the neutral which if you look on the cord should have some ribbing running along it. The hot side will either have some printing on it or be smooth, no ribbing. The side with the printing goes on the brass side of the socket, and the neutral or ribbed will go on the other screw of the socket.
As for the power in that room you will have to reset the circuit breaker which will usually trip when you screw up. Look for the red mark showing, shut off and then back on and that will usually turn the power back on in that room.
I'm not sure which switch you are talking about. The lamp socket one or one in the room you were in. Shorting out the socket will not usually ruin the socket, but if it is an older one that may have happened. If it is a switch in that room and does not work after resetting the breaker you may have burned out that switch.
If that has happened, I would encourage you to either seek out help before attempting a repair. You knowledge of electric devices does not seem to be adequate enough for you to try any more repair. The consequences could be worse.