Well, the first and most important thing to do is to not be ashamed. Everybody has to start somewhere, and anyone who decides to seriously take up some kind of cardio workout deserves to be commended!
One great trick to help you build up your endurance is to add one more minute to how long you jog every day. Whether you run outside or choose to jog on a treadmill, this is a gradual but quick way to increase your distance. It ensures that you don't push yourself too hard, but that you are also consistently improving.
Choose a comfortable length of time as your starting point, whether it be 30 minutes, 15 minutes, 5 minutes, or maybe even 1 minute! Start with whatever you can manage. This should be an amount of time that you can jog without pushing yourself to the point of exhaustion, because once your jog is up, you should finish the rest of your workout by walking.
Continuing to walk after you jog is a good idea if you find that you can't jog for very long. It allows your cardiovascular system to keep working and reaping benefits even if it is not working as hard as it was before. Walking the rest of your workout will make it that much easier to add one more minute to the length of time you jog for next time.
The amount of time you walk is up to you and depends on what exactly you want to get out of your workout. If your goal was to work out for an hour but you can only jog for 20 minutes, then walk at a brisk pace for the remaining 40 minutes. Walking is a great form of cardiovascular exercise as well, even if it is of a lower intensity than jogging.
By using the 1-minute method you will soon be jogging for much longer than you previously could. For example, if you run every day, than in only one month you will have added a half hour to your usual distance. In two months you will have added a whole hour! Even if you only jog a couple of times a week, you will still quickly see an increase in how long you can jog for, and, most importantly, you will quickly start seeing results!