The Annapurna Circuit Trek is said to be one of the top ten treks in the modern world. Although it's not a difficult trek technically, the demands of on the body of elevation (it has the highest mountain pass at over 17 000 feet) and distance (over 266 km), mean that you need to start out relatively fit aerobically.
Where to Start
You should assess yourself physically, by going to your family doctor. Once you get the ok, you can set up an exercise routine that will get you in shape to attempt this trek. You should start three to four months before your trek...The sooner you start the better.
The Annapurna Circuit is a 266 km hike going mostly up to 17,000 feet and then mostly down the same elevation. This means you will obviously need to strengthen your leg muscles. Your calves, quads, glutes and hamstrings are all going to need strengthening. Primarily, you should focus on squats, lunges, dead lifts, crunches and some back exercises at least three times a day with a day in between.
With so much walking uphill and downhill, you are going to need to get fit aerobically as well. You are going to need to do some form of walking, jogging, cycling, rollerblading or some other form of aerobics that uses your legs, at least 5 times a week. You should be building up to about an hour a session. You really need to get that heart pumping and in shape.
At least once a week, you are going to need to go on a hike of at least 8km with your hiking boots and backpack. The back pack should be filled with the same weight as you think you will be carrying on the trek, but if that is to heavy, you can work up to it. Your body needs to get used to the idea of carrying all that weight (between 25 and 40 lbs) for the 21 days the hike will take. Plus you need to get those hiking boots well broken in before you go to prevent any feet issues along the trail.
Just Before You Go
About a week or two before you leave for Nepal, give yourself a good rest from your training. Don't worry, you won't revert back to when you started, and your body will appreciate the rest. The last thing you want to do before you go is injure yourself while overdoing it on the training.
With a good base of physical fitness you should now be prepared to tackle the trek of a lifetime. Any additional fitness training will be had along the way as you climb slowly up the longest, and probably most beautiful hill of your life.