Your backcountry experience is affected by many factors. We just spent three weeks discussing one of them, gear. And later in the Planning Curriculum we will cover others, like food and the route.
This week, though, the topic is your fitness, and what you’re doing to improve or maintain it between now and the trip, i.e. your training.
My trips are categorized in two ways: (1) experience level and (2) fitness level. Based on the information you provided, you should have been placed on a trip that is appropriate for your known physical abilities. That said, you’ll enjoy yourself more if you arrive in relatively good shape (for you).
For time-tested data on average mileage and vertical for Low, Moderate, High, and Very High trips, please consult this page. Our expectation is that you will be ready to match these numbers.
For a discussion of the specific factors for which you should train (e.g. mileage, vertical, altitude, pack weight, off-trail) consult the lower half of the aforementioned page.
Alan has also written a good article, Quick and Efficient Training for Backpacking and Hiking. This approach (long weekend hike, short mid-week hike, higher intensity workouts on weekdays) gets good results, and it’s practical for people with busy lives.