Often a "multi-day back-packing trip" requires you to prepare physically for the miles, gain, elevation (reduced air pressure/reduced oxygen), and the weight you will need to carry.
I can wake up any morning and knock out a 8 mile hike at sea-level, however if I am going to the Sierra's and doing a multi-day, 7 miles a day trip, I know I need to train to make sure I feel physically prepared due to the significant differences in conditions, weight and distances. My rule of thumb is that a "Mountain Mile" is roughly 1.5 times as difficult as a sea-level mile - meaning an 8 mile hike with a back pack at altitude, will feel more like a 12 mile hike at sea level with a day pack - at least, that's how it feels for me. So, let's assume you don't hike but you have agreed to go on a back-packing trip. Here would be my advice for training.
You essentially want to:
Start 10 weeks out
Walk at least 5 times a week
Gradually increase distances
Gradually increase elevation gains
Incorporate one "difficult" hike per week
Incorporate a 20-30lb pack
Gradually increase difficulty and pack-weight
Peak 2 weeks before your trip
Walking is simply the best way to train for walking. Walking up hills is the best way to train for walking up hills, and walking up hills with a pack is the best way to train for walking up hills with a pack!
So, lets say I have been injured for a month (stamina dramatically reduces if you are not walking) and I am preparing for a 3 day x 8 mile hike in the Sierra's in 10 weeks and I need to start from scratch, my training would look like this:
Week 1. 4 x 2.5 miles x 0 EG 1 x 5 miles x 0 EG Total miles - 15 Total (EG) Elevation Gain - 0
Week 2 4 x 2.5 miles x 350 EG 1 x 5 miles x 400 EG Total Miles - 15
Total (EG) Elevation Gain - 1,800
Week 3
4 x 3.5 miles x 350 EG
1 x 6 miles x 400 EG
Total Miles - 20
Total (EG) Elevation Gain - 1,800
Week 4 4 x 3.5 miles x 350 EG 1 x 6 miles x 800 EG Total Miles - 20 Total (EG) Elevation Gain - 2,200
Week 5 4 x 3.5 miles x 500 EG 1 x 6 miles x 1,200 EG Total Miles - 20 Total (EG) Elevation Gain - 3,200
Week 6 (Use a 10 lb day pack)
4 x 3 miles x 500 EG
1 x 7 miles x 1,200 EG
Total Miles - 19
Total (EG) Elevation Gain - 3,200
Week 7 (Use a 10 lb back-pack) 4 x 3 miles x 500 EG 1 x 7 miles x 1,200 EG Total Miles - 19
Total (EG) Elevation Gain - 3,200 Week 8 (Use a 20-30 lb back-pack) 4 x 3 miles x 500 EG 1 x 8 miles x 1,500 EG Total Miles - 20
Total (EG) Elevation Gain - 3,500
Week 9 (Use a 20-30lb back-pack) 4 x 3 miles x 500 EG 1 x 8 miles x 1,500 EG Total Miles - 20
Total (EG) Elevation Gain - 3,500 Week 7 (Use a 10 lb back-pack) 4 x 3 miles x 500 EG 1 x 7 miles x 1,200 EG Total Miles - 19
Total (EG) Elevation Gain - 3,200