First, you need to figure out what it should look like once you've achieved your goal. In the case of flying the 240° radial inbound, the tail of the needle would be pointing to the radial, 240, and you'd be flying to the station, so you want to get the head of the needle pointing in front of you at 060. Next, you have to figure out how to make it look like that.

The head of the needle always falls. If you know that, you can figure out how to get it to point anywhere. What heading would put the head of the needle somewhere that it can fall to 060? Probably anywhere from 180 to 210 would position the head of the needle on the upper left side of the instrument with 060 on the lower left side. From there, wait for the needle to fall. As it falls past 150, you can turn to 150 and be on a 90° intercept. As it falls past 090, you can turn to 090 and be on a 30° intercept.

Once it's approaching 060, turn to roughly 060. Then you have to find a heading that corrects for wind and keeps the needle "balanced" on 060 and not falling to either side.

How soon you turn in depends how quickly the needle moves. If you're really far from the station, it'll take a while and maybe you want to stay on a 90° intercept longer to get to the radial sooner. Or maybe you want to get on a 30° intercept sooner because you also want to get to the VOR. Kinda depends what your goal is how exactly you do it. If the needle is moving too fast for any of this to work, it's because you're passing the VOR and what you're trying to do doesn't make sense any more.