It is best to charge a battery at the lowest current that a user can realistically tolerate, and then only recharge it when the remaining capacity has dropped to a level where there is an insufficient capacity left to deliver useful power.
In reality, this will usually result in a compromise between the longevity of the battery and the demand from the user. In medical environments where a portable dialysis machine needs to go with the patient as they move around a hospital, it is important that the unit can be recharged quickly rather than reducing the quality of care delivered to the patient.
A typical Lithium ion battery charges in two stages. In stage one, the battery is charged at a constant current and the voltage is allowed to rise. Once the battery reaches its maximum voltage limit (typically 4.2V per cell) the voltage is held constant and the current is allowed to taper down towards zero. Charge is terminated once the current has tapered to a pre-set level.
Here, it is important that the charging voltage is never exceeded. Because lithium-ion batteries consist of many cells in series, it is advisable to use cell balancing circuitry that shuttles the charge current away from the cells that reach their charging voltage first, allowing the others to catch up.