When it's raining, don't wear your leather jacket. If it does get wet, hang it out to dry right away before putting it away.
If you fold your jacket for an extended period of time, it might cause creases and cracks in the leather. Instead, hang it in a well-ventilated closet on a broad, ideally padded hanger.
Heat dries up leather, making it brittle and cracking. Never iron or steam your jacket yourself, and never lay it on or near a radiator or heating vent.
Leather will inevitably lose some moisture over time, but putting a good leather conditioner on finished leather can help it last longer.