How to measure the current drawn by the radio and the headlights from car battery easily?
@brhans has the most straightforward solution as a comment. Locating and getting a clamp around the wire may be a bit of a tricky endeavour in a car. An easier solution may be to just pull the respective fuses and put your ammeter in the terminals instead. Naturally before you go blindly plugging your meter where fuses were before you should check to make sure that the meter's fuse is rated higher than the current you intend to measure. The radio and headlights are likely to be on their own dedicated circuits so this should be pretty easy.

My meter's high current scale will only go to 10A; this is likely the rating for the radio's supply but the headlights may be on a 20 or even 30A circuit. You'll have to check with your car's manual and/or fuse panel insert. If your meter can't safely measure the current that the original fuse is rated for you might have to resort to other means to measure the current.

The process is simple: pull the fuse, connect your meter (set for current measurement) in the socket positions that the fuse was in, take measurement. You will want to make sure the lights/radio are off before you pull the fuse; opening a high current circuit under load can be unpleasant for you and the vehicle (arcing).

Clearly this is only intended as a temporary, vehicle-not-moving solution. If you want to permanently monitor the current then you can get a little more creative and use either inline shunts or a hall-effect current measurement device. Your question seems to indicate that this is a temporary requirement, so my first answer (pull the fuse and measure current across its sockets) is probably the easiest.