You could say this is the easiest part of a training program, but it is often neglected (how ironic!). Recovering properly from exercise is equally as important as the workout itself.

Your body doesn't actually get stronger or leaner while you are training, it does while you are recovering. For weight training, you should give the muscle group(s) you trained 24-48 hours of rest before you train them again. This allows the muscle fibers time to repair themselves and become stronger. However, on these "off days" you can perform HIIT or aerobic activities.

Individuals who work hard, but don't allow their bodies time to recover will eventually develop overtraining syndrome ("burnout" or "staleness"; exhaustion that persists even after recovery periods and can cause moodiness, difficulty sleeping, or depression), plateau, or become injured. Ultimately forcing them to take an even longer break from exercise.

Here are some recovery strategies:

Adequate sleep (7-8 hours is best)
Proper nutrition
Staying hydrated
Stretching post-exercise
Yoga/meditation
Massage (if a real massages is too expensive, try "poor man's massage" a.k.a foam rolling!)
Epsom salt baths

You won't hear your trainer telling you to rest or "take it easy" often, so take advantage of it and get some quality rest!