There's no simpler way to say this but JUST START!
That's the best way!
Anyone can run, we all have the right equipment - it takes no fancy gear or special physiology - we are human, therefore we are all 'natural' runners. The key is to train your body to adapt to moving your body quicker than usual.
Start by making a commitment to yourself - this is where signing up to a couch to 5k programme OR signing up to a 5km fun run (like Race for Life or Parkrun) can really help to motivate you and keep you on track.
Decide a time and day that you can keep the same every week and make it a DATE WITH YOURSELF promise yourself that you will do every session without fail. A group doing this together comes in so handy as you can help each other stick to it. Maybe you can find a friend who also wants to get into running and you can do it together.
It is easy to get carried away and say "i'm going to run everyday for the next 4 weeks" but this is a guaranteed recipe for disaster. Firstly you'll probably injure yourself, secondly you run the risk of it being too hard and demotivating you!
A good beginners programme will involve lots of running and walking intervals and a GREAT programme will have drills and information on your form.
Figuring out HOW to run correctly (using your glutes, core and with good posture) will help you so much in the long run and will prevent injury.
Aim to start with 1 run/walk per week (with the running increasing in time and the walking decreasing over a period of 6-8 weeks) and try to have a second exercise day where you either do additional run/walks, cross training (yoga is ideal!) or just walk!
Listen to your body
There's a difference between challenging yourself and pushing yourself beyond safety/comfort. There's no doubt that to change what your body is used to (probably walking) into running (5km without stopped for example) you will need to challenge your body. Discomfort is OK pain IS NOT. If at any point you feel actual pain as opposed to discomfort such as being tired, muscles starting to burn, feeling out of breath, feeling your heart pumping. All of these things are NORMAL, but if you start to feel PAIN - stabbing, aching, feeling tight then it's time to stop.
Slow down rather than stop - let's say you are doing 4 mins running and 2 mins walking. And you've just gone over the 2 minute mark running and your whole mind is telling you to stop - your mind is lying! You absolutely CAN go all the way to 4 minutes - your mind is just rebelling against this change of pace - EVERYONE EXPERIENCES THIS - from the guy down the road to Paula Radcliffe! You absolutely CAN carry on and the way to achieve this is to tell yourself that and also you can SLOW DOWN. I don't care if an arthritic snail could go faster than you, it doesn't matter - this isn't about speed. It's about teaching your body to stay in 'jog mode' for longer and longer each time. And the best thing? It won't be like this for very long - you will find if you persevere 2 mins jogging will become 4, will become 8, will become 20 or 30 minutes!