Combo of nutrition, long runs, and interval training
Endurance is a combination of using your available nutritional resources effectively, being able to run for a long duration (typical association with endurance), keeping a relatively low heartrate, and also maintaining a speed for a long time without fatigue. The mistake a lot of runners make is that they focus on running for a long period of time and ignore things like heartrate, proper nutrition, and speed maintenance.
You should be augmenting your diet, if you're looking to run farther. You need lots of clean, high-fiber carbohydrates like fruit and whole-grain bread/rice to keep your energy high for a long period of time. When you eat processed, sugary carbohydrates, you will burn this quickly and run out of energy while you run. You should also eat lean meats/protein, take a calcium supplement or eat/drink dairy to protect your bones, and ingest healthy "fats" like almonds to protect your organs and joints.
Next, you should be doing a combination of at least three cardios per week. Only once per week should you be extending your distance or time. If you are training for a running event, you should be increasing your distance by about .5 miles or about 3-5 minutes per week. This will protect you from injury but challenge you. Start at a time where the last 5 minutes of your workout you are very tired. You need to challenge yourself every week--making large gains means not easing up as it gets easier. Your long run of the week should be 5 minutes past being tired. Twenty minutes for an active individual should be an okay start, though I would gauge how you feel (the last 5 minutes very tired approximation) instead. I would not mix in intervals with this--it should be the same speed throughout.
The other cardios should be one very long cardio, like going for a long walk at an incline or a long bike ride. It should last about twice as long as your long run, but shouldn't be as hard. This will build your muscles to withstand long duration cardio.
The last cardio should be intervals. When your runs get up to 45-60 minutes at a time, you could include one session of HIIT instead of intervals. With interval training, you want to mix in jogging and running with walking at speeds slightly faster than your long run speed. The idea is to get your heart-rate up and then recover. This will make your heart stronger for the longer duration runs. It will also most likely increase your speed or make your current speed easier.
Any additional cardios you fit in each week should be shorter, steady-state cross-training cardio to prevent injury. This could be 20 minutes on the elliptical machine, 20 minutes on a bike, 20 minutes jumping rope, etc. Increase this time as you increase your long run time--it should be shorter than your long run (e.g. if your long run is 60 minutes, you should do 40-45 minutes of cross-training).
Heart-rate training is fantastic, too. I increased my speed/distance simply by watching my heart-rate. The idea is to slow down if your heart rate gets too high and let it recover (by walking for a minute or two). Too many people just "kill" themselves trying to get to a distance and don't ease into it. As a result, they end their sessions completely exhausted, light-headed, or they puke. This is a sign that you're doing something wrong. Exercise should be very challenging but shouldn't make you ill.
Good luck!