Yes this something a competent DIYer can do themselves. Here are the steps.
Tools required - Adjustable spanner. Water pump pliers (plumber's grips). Radiator bleed key. Shallow tray. Bucket. Old towels.
- Close both valves of the radiator. The TRV (where you adjust the temperature) can be screwed closed to 0.
- Pull the cap off the valve on the right (lockshield valve). It should pull straight up and off. Use an adjustable spanner or grips to close the valve spindle down in a clockwise fashion. Count the number of turns to close it and make note. You will want to open it up the same amount of turns when put back into service.
- Open the bleed vent at the top of the rad, keep an old towel handy and catch the dribble of water that may or may not issue from there. When there is no air or water coming out of the bleed screw, you have proved the valves are not letting by and it's safe to drain the radiator.
- Use your grips to hold the body of the lockshield valve tightly and an adjustable spanner to slowly undo the nut closest to the radiator NOT the nut connected to the pipe.
- Water will start to trickle from the radiator valve area. Catch the water in a shallow container and keep a bucket handy to empty the shallow tray into as you go. Or use a wet vacuum if you have access to one.
- Don't rush, you may need to gently pry the valve away from the rad to get the water to flow out. Don't use much force. Do that slowly and carefully, you don't want to pull it completely away, just open up the gap to control flow of water.
- When the water stops flowing you can undo the other valve (TRV) in the same way and lift the radiator off its brackets. It should pull upwards and off the wall. Do this over the old towel as it may drip black sludge on the floor. Tip the last of the water from rad into bucket.
You can then reattach the radiator brackets into the wall and do everything in the reverse order to get it back on.
If the radiator is going to be off the wall more than a few minutes you should cap off the open ends of the valves with a 1/2 inch female blanking cap incase one of them lets by.
Post again when you want to reattach and we can advise further if you have any concerns.