One for the ladies - make sure you have decent sports bras.
Invest in some technical clothing. This doesn't have to be expensive, there are plenty of companies who sell running specific kit that won't break the bank!
Get into the habit of warming up before & warming down after your run.
Take walking breaks if needed.
Build mileage gradually.
Go for distance rather than time. Slow it down, be patient & don't worry about your pace or time.
Safety in Numbers
Join a running group - use the experience of people who have been there, done that! Most running clubs have several groups training at different distances & speeds at their training sessions.
Alternatively use a Couch to 5k app or find a local group that start you from this point.
Nutrition & Hydration
Don't eat just before a run!
Try & eat within 30 minutes of finishing a training session with a mixture of protein & carbohydrates. Don't overdo it though if you are just starting out, the longer/more intense your training session the more attention you will need to pay to your nutrition.
Make sure you stay hydrated throughout the day especially on a training day & rehydrate post training session.
Mix other types of training into your week such as weight training or do a regular Pilates or Yoga class.
Make sure you have rest days!
Keep a training log to make running a habit
Set small achievable goals on a regular basis to progress your training & keep it interesting!
Listen to your body! Running through pain is never a good idea. If you do have any pain during or after running, take some time to rest & if the pain persists see a therapist or your GP to get some advice.