I see lots of people talking about HIIT, what is it?

High Intensity Interval Training

It's a method of aerobic exercise where you alternate periods of high exertion with periods of less-intense activity. For example, when running, you might sprint quickly for 30 seconds and then jog slowly for 30 seconds, then repeat the pattern for a specified period of time.

The idea is that you can improve your aerobic capabilities by "pushing the envelope" during the intense portion of the workout, while letting your body "recover" during the less intense portion. You end up burning more calories in a shorter period of time, and gain more benefits long-term because of the elevated metabolic rate you maintain after the workout is done.

Not recommended for the beginner or the weak of heart, HIIT is a great way to get a good workout in a short time period and build better fitness.

Say if you were going to run 1 minute and then walk 1 minute... how long should you do this to achieve a GOOD workout?

Most things I've read suggest that you start slowly and work up to higher levels. Using your example, I would say to jog for 5 minutes to warm up, then do three "intervals" (run 1 minute/jog 1 minute/run 1 minute/jog 1 minute/run 1 minute), then jog for five minutes to cool down. That would be fifteen minutes of total exercise, and about equal to a half-hour of traditional jogging in terms of calories burned. The long-term effects are definitely better.

You might not be able to do this, even if you can now jog for a half-hour. As I said, start slowly and work into the routine. It's a lot harder than it sounds if you are doing it right... you should be going almost full effort when you run, and just barely more than a walk when you jog. You don't have to go with a 1:1 ratio either... you can run one minute then jog two if that helps you recover. You can also go by distance rather than by time... for example, run a block then jog two blocks.