Best is subjective really, so the "easiest" way I found was to just blow it out and run some hot water
through it and blow it out again. Boiling mine lifted the finish so I've not done it again since.
Some people use isopropyl alcohol, some use vinegar, some use lemon
juice... if you take something that's going to help lift the gunk off and soak the atty in it for a while it'll probably help some no matter what you do.
I'd consider the best as being the most thorough but it's also the hardest. If you can lift up the spike, plate and wick, you can clean the wick very well any way you like. Some rinse it, some burn it, some soak it. It's difficult to do and really fiddly but it's likely the "best" way. Mind you, I wouldn't do it often either, maybe once a fortnight to a month.