What is the fastest way to increase stamina?

Try some sprint training x 2 a week simply put just run 50-100m as fast as you can with a 2 minute (or whatever leaves you ready for the next sprint) and do 5-10 sprints.
Then do the interval that Anuyoo below suggested.
Tim Walker BSc

When you say you failed miserably do you mean you couldnt run 1500m?
There are alot of things you can do but i will need more information as to what happened and the time it took you. Yes you could try sprints that would work but also your running technique might be pants and need work so if you are serious about wanting help then email me at info@dosctraining.co.uk and i can write you a programme for you that will work.

Your best bet is to train specifically for running that distance! Get a trainer to assess you properly and write you a progressive programme including relevant sports conditioning drills and also get your nutrition right.
Other training like kettle bell routines with an appropriate weight can help you develop stamina and cardiovascular endurance and will also train the posterior kinetic chain, very useful for sports and athletics. There is a good website to explain the benefits, see source.

Interval training would be a good option for a race like the 1500m. Get yourself on a treadmill, put on a slight incline (to work your legs that little bit harder) and work to 30 seconds bursts of fast running to recovery jogging. Do this for 6 - 8 minutes. You should be busting a gut by the end but that's the objective. The sprints will train your body to get better at transporting oxygen to your muscles so they are more efficient when you run. This in turn will improve your anaerobic fitness (without oxygen) and your aerobic (with oxygen)
Do this 2-3 times a week and it becomes easier, increase the fast running/spring time from 30 to approx 45 seconds, with 30 at recovery jogging pace.
Note: it's important you continue to jog throughout the exercise, this is to mimic proper race conditions. Recovery jogging pace should still be about pace 9/10 on the running machine.
You could increase the training time from 6-8 minutes as you get fitter, but this will push you into longer distances like the 3000m. I'd suggest squeezing the training time down to 5-6 minutes and really pushing yourself hard, then you'll be on track for a decent 1500m time in an actual race.
Every now and again mix up your training, so rather than the treadmill, jump on a bike instead and do similar intervals, but add some heavy resistance (really feel the burn in your legs) so you're standing up off of the bike seat and powering through.
Good luck!