If I power-walk rather than go running, how long should I walk for each day?

As with all exercises how often, how long and the intensity level is down to the initial fitness level and health of the client. As a general rule I would suggest starting with 2/3 walks a week and build up to as your fitness levels increase.
The duration of each walk will depend on whether you are taking the same route everytime or different routes taking in different surfaces and inclines. If you are able to walk somewhere scenic; park, forest, hills, beach etc you will be less concerned about the duration and would be more inclined to walk for longer and enjoy the exercises more.
Try for 20 minutes to half an hour initially, if you do get fatigued you can always slow your pace or stop for some light stretching.

30 minutes 3- 5 times a week

Hi you should walk at brisk pace preferably with 1kg handweights and aim to power walk for a minimum duration of 30mins. Try to find a course which involves hills to make the session varied..

Power walking should be a long duration activity if it is to exert a meaningful effect on the body and produce results (fitness, weight loss). The duration depends on the how often you are able to exercise. 45 mins at 4 X per week or more. If exercising once or twice a week power walk for 1-2hours. gregbatchelor.com

I'm a firm believer in cross training , which is to say , do a variety of different cardio exercises .
power walking is great as it burns calories , increases cardio strength and gets you outside ( unless you're on a treadmill ) . Each session is best to do for a solid 60 mins , the longer you walk the more calories you will burn . At the end of your session use the cool down period to stretch all of your body with focus on the legs and gluteals . I suggest 5 power walks a week for 6 weeks then review your routine . Remember also that strength training is a great way to increase muscle definition / tone so include 2 x 30 min full body strength training sessions ,alongside a healthy food plan this will increase positive results .

Power-walking is more effective than most people think. I test a number of my clients to see exactly where their peak 'fat-burning' zone is - for most of them, it occurs around 120-125bpm and they are power-walking at this point. However, this is only true for around 80pc of clients. In any case, my article on "what is the best exercise for me?" goes into more depth. (Article can be found on link below).