What kind of phone are you interested in? Some specific model, or just a cell phone in general. Typically the battery is charged like any other battery. The phones microcontroller monitors the charging process to prevent overcharging and basically put the power adapter feeds a constant current into the battery until it is fully charged.
You can find service manuals for many different cell phones using google. I happen to have one from the Motorola V3 Razr so its attached for your viewing pleasure.