What is the best way to charge phone's lithium-polymer batteries to optimize battery life?
You can apply the same rules to both Li-ion and LiPo batteries. Regarding your question, the parameters under your control when charging a cellphone are the state of charge (%) and the temperature. Lithium technology lifetime suffers in &quot;high energy&quot; conditions, i.e. high temperature and high state of charge. So I can give you two &quot;ideal&quot; advices:

try to keep your phone's temperature as close as possible to 25°C (especially when charging);
keep the state of charge inside the 20-80% range, whenever you can afford it.

Bonus tip: prefer charging at low current rate, whenever the charging time is not of the essence, for example using a 1A adaptor instead of an high current adaptor. Low current means less heating of the battery.
Other considerations:

be careful when charging by means of wireless charging (e.g. Qi): a low quality charger may produce a lot of heat, and this would be a problem since the battery is in direct contact with the charger;
be careful when charging inside your car; a typical scenario is hanging the phone to use google maps for navigation, while charging: this is quite bad because you are charging while using lot of processing power (which means heat) and the phone is exposed to sunlight (which means more heat).