From Stockholm:

We recommend train and bus for the environment. 

With train and bus:

Take the night-train from Stockholm to Umeå, change to bus towards Hemavan/Lycksele. Change bus in Lycksele towards Sorsele/Ammarnäs.

With flight:

Fly with NextJet to Arvidsjaur. Change to bus towards Sorsele, change again to bus towards Ammarnäs. OBS! Few flight departures that fit with the bus. Fly to Lycksele and rent a car.

By car:

Via Östersund och thereafter E45 towards Sorsele. In Sorsele drive towards Ammarnäs road 363. Alt via Umeå och thereafter road 363 towards Sorsele/Ammarnäs.