Training to complete a mile-long swim is not as difficult as it sounds, as long as you have the drive to stick with a training program and are willing to change your diet. You don't even need a trainer or any special equipment. As long as you don't have any health problems and are already in relatively good shape, you should be able to train yourself to complete a mile swim in a little over a month.
Change your diet so it is high in lean protein -- like chicken and fish -- and low in fats. Your body is going to need the right foods to build muscle and burn fat while you're training. In fact, the food you put into your body is more important than your training. You will not see the results you want without a diet suitable for someone training for a mile swim.
Choose three days a week to swim. You do not want to add any more days to this weekly routine because swimming is strenuous exercise. You need the resting days in between, so your body has enough time to recuperate and build muscle.
Set a goal of trying to swim at least one hour non-stop. This is about how long it takes to swim one mile.
Start your timer. The first time you start training, record how long you are able to swim before you have to stop. This will give you a good indicator of how much longer you'll need to swim in order to complete one mile.
Continue swimming three days a week for at least one month. During this time you should be trying to increase your longest swimming time. Also, don't be afraid to mix up your swimming routine if you get bored. Boredom is one of your worst enemies, as it will likely reduce your commitment to training. Try swimming as fast as you can for a short distance, with small rests in between or design your own swimming game. The most important thing is being engaged and focused on increasing your endurance.
Stop training two days before your mile swim. You'll need this resting period for recuperation.
Warm up and stretch anytime you are exercising, to prevent muscle injuries.