Full-grain leather is the only material in a wardrobe that genuinely improves with use. The patina it develops is a record of where it has been.
Do almost nothing, most of the time
Wipe with a dry cloth after use. That is the whole routine for the majority of the year. Over-conditioning is far more common than under-conditioning and leaves leather soft, saturated and prone to stretching.
Condition twice a year
Use a small amount of neutral conditioner, worked in with a cloth, and let it rest overnight. If the leather still looks glossy in the morning you used too much.
When it gets wet
Blot with a dry towel and let it dry at room temperature, away from any heat source. A radiator will make leather crack permanently within one drying.
Storage
Keep bags stuffed with paper so they hold their shape, in a cloth bag rather than plastic. Leather needs to breathe.