There are two things required to climb/ski above 10,000' elevation in Mount Rainier National Park:
1.) Each individual must pay the Climbing Cost Recovery Fee (good for the calendar year).
You can pay before coming to the park. To pay the fee, you must visit the Pay.gov website, submit your payment information, and receive your confirmation email. Save your receipt and bring a copy with you when you register for your climb as proof of payment.
Pay the Climbing Fee
2.) Each climbing party needs to obtain a Climbing Permit. This includes climbers who are attempting single-push climbs as well as ski mountaineering on glaciers above 10,000 feet elevation.
All of the climbers on a team must have paid the Climbing Fee before a Climbing Permit can be issued. Only one permit is necessary per team for each climb.
All Climbing Permits must be picked up in-person at a ranger station.
Currently, 1/3 of all the permits are saved for walk-ups (climbers registering not more than 24 hours in advance of their climb). There is a non-refundable $6 fee for walk-up permits. Note that this is separate from the cost-recovery fee.
Reservations for most permits (about 65% of all the permits) are available in advance through Recreation.gov. Note that once you've confirmed a reservation for a climbing permit, you must still register in-person at a ranger station to pick up your permit.
If ranger stations are closed for the season, climbers must pick up their permit at either the self-registration kiosk in Paradise or at the Longmire Museum. This option is NOT available during the summer/spring climbing season.
Check the park's website for more details.