Here are some basics regarding sensible Running:

Limit to no more than 3 times per week

Purchase appropriate footwear

Stay mentally and physically relaxed

Move naturally/keep consistent stride

Keep form neutral and relaxed

Run within your limits/biomechanics

Avoid ball first or heel first impact

Keep a rhythm and pump arms

Stay alert

Wear a heart monitor

Change things up (duration speed, course, days, etc)

NOTE: Tai Chi can also be a great warmup for running.