I'm a flatlander (Minnesota) - a few things that work well for me:
- Long efforts on the trainer (I never coast on the trainer),
- Long efforts on rail-trails - great with power meter, but without power meter, just keep the heart rate in Z3-Z4 - no coasting
- Ride steep local climbs seated to train yourself for the body position while climbing
The one thing I know I'm missing is riding in thin air ... if you're going to high elevations, that'll come down to good cardio conditioning.
Here to point, the biggest climb I've found myself riding was back in March - 1,200 ft climb averaging 5% with kicks over 15% and mixed surfaces (gravel & paved). I had no issues climbing, and could have kept climbing if I had more time and more hill to climb. This climb started at sea level, so I didn't have to deal with thin air.
I have my sights set on climbing Mauna Kea (13,800 ft climb from sea level). Prior to that challenging, I'll drive to Estes Park to ride Old Fall River Road (5,000 ft climb summit at 12,000 ft) to train at altitude.