Multiple lithium cells in parallel will appear as one larger cell to the charger, so no more complicated to charge than a single cell. That said, make sure they are within a few mV of each other before connecting them for the first time, and ideally they should be the same type of cell.
Cells in series is where it gets complicated because you really should use balance charging if you want the pack to be reliable and safe.
The constant current mode basically involves limiting the charging current to the cells until the voltage rises to 4.2V (or a bit less to reduce wear on the cells if you don't need every last bit of the capacity). The current limit would mostly depend on the capacity of the cells you are using.
Then you just keep supplying that voltage until the current drops to some value below 10% of the limit (determined by how full you want the cell vs. how long you want to wait for the charging to end), then you cut off the power - trickle charging is bad for lithium cells.
As for the actual implementation - I would personally look for a li-ion charging chip that meets your requirements first. It would make the charger design simpler and possibly safer. As Audioguru mentioned, cells that have been discharged too low can be dangerous, and at least some of these chips are built to handle these situations.