Transition back into running
There is certainly going to be a transition phase where your legs get used to running again, the likelihood is you won't notice until the following day. You'll probably wake up with very sore legs as you'll have used muscles in the legs and exerted yourself perhaps a little too much. This is why you need to build it up slowly, and forget where you left off. Jumping straight back into 60 miles or 100km a week and running 3 sessions a week is more likely to get you injured rather than super fit.
Check your running shoes
If you have not run for quite some time then before you start back up it might be an idea to look at the state of your running shoes. It is a good idea to invest in a new pair as this will ensure there is a decent level of cushioning and support (if needed) and will prevent injuries. Think of it as a new start, and buying a new pair of shoes will mean you have to go out running!
Forget the level you were at before
As I mentioned before it is a good idea to forget all that you have done before when it comes to running, as you are not going to be as fit as you were when you stopped running previously. You need to be patient with the build up and make sure you don't rush things and increase your weekly mileage too quickly.
Enjoy your running
Everyone should enjoy running and in order to improve this is the number one piece of advice I can give. Try and think back to why you stopped running last time, was it work commitments? Were you spending too much time running and not socialising? Or were you just fed up of simply running miles and getting bored. Once you have remembered why you stopped the first time, then you need to plan on making sure this doesn't happen again.
Run with others
Running is always easier with friends. Join a running club or group and this means you can run with others. There are so many running clubs now that there is bound to be one close by, and believe me they are not all full of serious runners who are training for the Olympics! You'll probably find a group that heads down the pub afterwards - however that might be why you started running again, to stay out the pub! Everything in moderation, that's right isn't it?
You don't have to just run as part of training, you can swim, bike, cross train and even do just circuits. If you want to improve your times in the 5km/10km distances then doing other forms of exercise can really help your overall conditioning and prevent overuse injuries.
Introduce structured sessions
When it comes to actually running introduce some sessions into the training program. Faster periods of running with recovery time in between can really bring you on rather than just jogging round the park for 30 minutes at a time. Talk to other runners and see what their training is like and what works for them. Running is very much trial and error until you find what works for you, this is the same for coaches as well. They experiment with athletes until they find the right formula.
Enjoy the running, set some goals and know that improvement is just round the corner!