1st off.... welcome to ECF!
There's a lot of hardware makes/models out there so I can only speak in generalities.
The chargers that come with them auto-shut-off when charged (it's really how all Li Ion chargers work). Keep them same-to-same tho (use what came with it) since some manufacturers swap polarities, or other such nonsense.
The light on the end should go on when charging and off when done. Sometimes there's a little light on the charger itself that changes color and/or goes on/off.
You'll get more specific answers if you post a link to the particular make/model... if this doesn't do it.