Summarize:

This training plan will allow you to slowly increase the amount you can comfortably run, over the course of four weeks.  Each week will add more distance and time to your jog, allowing you to meet your goals.  Try to follow this schedule for your first week:  On days 1, 3 and 5, do four sets of running 1/16th of a mile and walking 3/16th of a mile. On days 2, 4, and 6, rest or cross train. On the seventh day, take a break. During the second week of training, you will increase the amount you jog and decrease the amount you walk.  This will allow you to progress towards your goal of running one mile, without over stressing or over training your body.  Follow this schedule for your second week of training:  On days 1, 3 and 5, do four sets of running 1/8th of a mile and walking 1/8th of a mile. On days 2, 4, and 6, rest or cross train. On the seventh day, take a break. During the third week of training, you will be approaching your goal of running one mile without stopping.  This week will continue increasing the amount you are able to run and will continue to build cardiovascular endurance.  Use this training schedule for you third week of running:  On days 1,3 and 5, do four sets of running 3/16th of a mile and walking 1/16th of a mile. On days 2,4, and 6, rest or cross train. On the seventh day, take a break. Week four is the final week of your training program.  You will be able to run a full mile by this point and will be doing so over the course of the week.  Enjoy your accomplishment and keep your running routine strong by using this schedule:  On days 1,3 and 5, run 1 mile. On days 2,4, and 6, rest or cross train. On the seventh day, take a break.
Start your first week. Move into your second week. Keep pushing into your third week. Run a mile on your fourth week.