I have exercise-induced asthma. That basically means I'm fine under most conditions, but at a certain point I start coughing and having some trouble breathing. I used to be a distance runner, and I wasn't diagnosed back then. What that usually meant was that I was fine during training, but during competition when I pushed myself a little harder than normal, I'd start having trouble breathing toward the end of the race (which would usually lead to coughing, collapsing to the ground, then getting up and finishing the race).
I recently started using a rowing machine. What I found is that up until a certain level I'm fine, but after that point, I have issues. Now that I've done it a few times, I have a decent idea exactly where the intensity starts to trigger the bronchoconstriction.
You may want to use a heart-rate monitor so that you can tell where things start to be an issue for you. The more time you spend just short of that trigger point, the better off you'll be. That way you can keep progressing both in time and pace, without triggering episodes.
Basically as nighthawkz said, start slow with walking, then move to a slow run, and then keep pushing the pace as your cardiovascular system adapts to the training. You can start with a 10 minute session, then push it to 15 minutes, then to 20 minutes over time. I really don't see any reason to go over 30 minutes for cardio in a given session -- at least for fitness purposes. I personally think it's better to have more frequent sessions than longer sessions.
As far as medication, the adult and pediatric recommendation seems to be a puff from the [albuterol] inhaler about 20 minutes before exercise.