to take off an old radiator you first have to turn off the valve at each end of the radiator by screwing them down clockwise tight as far as they will go. one of the valves will have a smooth conical shield on it, you have to take this shield off to get at the valve, you will need a spanner or pump pliers to close it.
note that if one of the valves is thermostatic then simply turning it to 0 is not enough, you have to remove the head and screw on the blanking cap you would have got when the valve was bought ( not much chance of you having it ) otherwise if you have a very cold night then the valve can open up and flood your house. if you do the job quickly however i.e. old radiator off new one on straight away then you should be ok with just turning the valve to 0.
right, now you have to drain the water that is inside the radiator still. place a small bowl or frying pan under one of the valves (have a bigger bucket nearby ) and open the nut at the side of the valve until the water starts running out, if the water slows down the open the air vent in the rd to force the remaining water out, when you think its all out tilt the rad slightly and the last bit will flow out.
you should already have bought a new rad, try to uy one as near to the length of old one as possible, go very slightly smaller rather than larger is you have to as you can extend the inlet pipes if needed. you are going to have to insert either new or the old inlet connections into the new rad using ptfe tape on the threads and then hang the new rad and re-make the joints.