With regardsto charging li-ion batteries, the above answer is completely correct, however,
Most phones control the charging of their batteries within the phone itself, and all we have to do is supply a 5 volt, 500-1000mA power supply to it via a USB connection. The phone then uses a buck converter to lower the voltage to 3.0 - 4.2 volts to appropriately charge the phone.
So if you can find a small solar panel that produces the 5 volts, and you then solder the correct connections to it so you can connect it to the normal USB connecter/charger port to your phone, it MIGHT work. I say might because it will depend on what type of amperage you can supply. Some phones will charge at lower amperages, but some will not even attempt to charge until a minimum charge is obtained (For example, I have played around with solar panels and charging iphones and it seems like the iphone won't start charging until it gets 500mA, but sometimes it will keep charging, although very slowly when that current drops below 500mA)
And you don't have to worry about the "trickle charge". Once your phone's battery is full, it will stop accepting charge from the solar panel whether you unplug it or not.