Do you live to ski, or will you be teaching to live?
Are you certified? What level?
Certification is an important detail, as most resorts will assign lessons based on your qualifications and experience. At my resort, you need to be level 3 to be in the private rotation. Instructors with no cert., or level 1, will teach young children in beginner group lessons. Level 2 instructors teach older kids groups, adult groups, and some privates.
If you are living to ski, you may need more than a level 1 to actually teach an accomplished skier. But if you are teaching to live, you can earn a steady paycheck ($400.00/wk) and a few tips with a level 1. If you are a level 2, you will be paid more hourly, and make more in tips, but may not work as many hours your first year.
How will you get paid for requests? Some resorts give you a percentage of the cost of the lesson, other resorts give you an add-on that goes up depending on the number of requests you receive. Some resorts don't let you teach a request if you are scheduled for groups that week.
Will you receive a per student add-on in group lessons? At some resorts this add-on can be an additional $50.00/day. Teaching a group of 8 kids is harder than a private, and the resort is making more than they would for a private, so you should make more as well.
Research the resort's clientele. Considering our present economic situation, will the resort you are considering still attract students who can afford to take lessons? Is the resort primarily a group lesson type of resort, or private? How long are the lessons? 1 1/2 hr. group, half day group, or half and full day privates? There is usually unpaid down time between group lessons which can cost you as much as two hours a day if you are teaching 1 1/2 hour lessons. This all factors into how much, and what kind of skiing you will actually be doing, and how much you can make. You should get tipped teaching groups, but not nearly as well or consistently as privates. In full or half day privates you can see anywhere from $40.00 to $100.00/half day and $80.00 to $200.00/full day in tips if your resort is heavily biased towards privates.
If you live to ski, you may not want a busy resort because you may have too much work. If you need to teach to live, check to see if the resort is busy enough in non-holiday periods to keep you teaching. Will you be assigned enough lessons in January to make it until February. There is a resort near me that pays 30% more hourly, but doesn't sell enough lessons to keep instructors earning more than a part-time wage.
Ask if you will be paid for showing up when you are scheduled, but don't get a lesson. Gas is more expensive in the mountains, and you may have to live some distance from the resort. I know instructors who drive 120 miles round trip a day and don't always get a lesson. Three days like that = a tank of gas and no income. Are you permitted to ski while you wait for a lesson, or if you don't get a lesson?
There have been some very good suggestions already offered on questions you need answered. The most important question is one you need to answer. Will you being doing this for 1 year, or years to come? It takes a few years to develop a base of return customers. In that time your hourly rate will go up, and your add-on for requests should also go up. You will have moved up the "totem pole" so to speak, and will have less down time. It is quite likely, that if you give it 5 years, you will double how much you make in a season compared to your first season.
If you are doing this for a year, choose a mountain you dream of skiing, and teach the lessons you are assigned. If you need to teach to live, and make some money for new skis, get the highest level of certification you can before you move. Choose a mountain where advanced beginners and intermediates take private lessons. Experts take lessons, but not enough to keep gas in your tank. Make sure that the resort has good beginner and intermediate teaching terrain, and runs that will keep your students safe, interested, and progressing when they are on their own.
BW is correct that with a level 3 you can average over $200/day at a busy resort, but at that same busy resort it may take more time to attain level 3 because you are too busy to train for the exam.
Best of luck.