From page 252 of "Achievement of a Rainbow Light Body Volume 6," a book by Grand Master Lu
The incense that we use to make offerings to the Buddha comes from many sources -
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When one lights the incense, one should not blow out the flame with one's mouth. This is because one may have impure breath, and blowing out the flame with impure breath will pollute the incense. One should instead use one's hand to put out the flame. Since many people suffer from oral diseases and have bad breath, it is always better to avoid using one's mouth to blow out the flame of all incense and candles.
Also, if the incense sticks extinguish half way through, it is better to remove the incense rather than rekindle it, for this is not a good omen. According to tradition, an incense stick should be burned from the top to the bottom. If it extinguishes in the middle, simply throw it away.
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There is much to know about incense. I mentioned "emergency incense" before. That is when you have an urgent matter, and need to immediately entreat the help of the Bodhisattva. Normally, we light one end of the incense stick. During such an exigency, we may light both ends of the incense stick, then place the stick in the urn. The passing Bodhisattva will stop to listen to your urgent request. So there are "emergency" incense, "headless" incense (incense that is half-burned), and "discharging" incense (incense that is put upside down in the urn).
It is virtuous to offer the best quality of incense to the Buddha. Incense that is of poor quality will give off a bad smell, and may affect one's health. Therefore, it is important to know the quality of different kinds of incense.