For sealed systems, seek the services of a professional heating engineer
If for one reason or another you need to replace a radiator, it is obviously easier to fit a replacement which matches the old one. In this case, you will need only to drain down the radiator itself rather than the whole system. See the pages on removing and refitting a radiator. However, more often than not, you can only get one of a slightly different size or pattern.
Measuring and fixing the radiator brackets
Drain down the system following the guide for this and remove the old radiator. With the new radiator on the floor, mark a centre line between the fixings on the back. Mark a line on the wall for the centre of the new radiator.

Now, place the brackets on the back of the radiator making sure you have them the right way up and carefully measure how far they are from the centre line. Now, carefully measure the same distance from the line on the wall to give you a vertical mark for each of the brackets.
Allowing between 4 and 6 inches from the floor to the bottom of the radiator, measure how high up the wall the brackets need to be. Place each bracket on the wall in turn and mark the fixing points. Drill and plug the wall then screw the brackets in place. Make sure you have good solid fixings
Remember to check for pipes, cables etc before drilling.
Adjusting the heating pipes

Lift the radiator onto the brackets to determine what alterations are necessary to the pipe work. Lift the flooring and cut the flow and return branch pipes below the floor level. Fit the valves to the new radiator and hang on its brackets. Loose fit a short length of pipe to the bottom of each valve to help you assess what alterations are necessary to the pipework. Then, using either compression or soldered fittings connect up the flow and return to the respective valves.
Remember, with soldered fittings, the flame from a blow torch is a major fire risk. Take care, and refer to the soldered copper pipe section for further advice.
Once all work has been completed, refill the system and check for leaks.