Probably just run them under water and let them dry, possibly use a bit of kitchen towel or tissue to help the process along. To be honest I'd just fill them up. Residual flavour should disappear quick enough unless its menthol
The reason I am asking is I am starting to get a slight burnt taste, and thought a proper clean may help. Should I use some boiled water for the clean? pouring in from the top?
If you have it for more than a week or two my suggestion would be to just replace it as they are a consumable and I've tried every method of cleaning and dry burning but the best advice is just replace it for what they cost.