In very basic terms (which I recently posted in another thread); my approach is...
Running faster than you need to over distances shorter than 2km (typically any distance up to say 1.5km)
Running slower than you need to at distances over 2km (any distance you like really)
And also practising 6 minute km pace frequently, so your body and mind gets very familiar with it
Just to add to this.
First do a Cooper test and find out your 'cruising speed' this is the pace you can comfortably run the test in, you know you're running, but you're not straining yourself. Don't worry about distance at this point. Judging by your post it's likely to be somewhere between 6 min15 sec per km and 6 min 45 sec per km. Use that as your baseline.
Your 'easy' longer runs you should target around 1 min per km slower than your cruising speed. It's harder than it sounds as your natural instinct is that you can easily run faster. This will help your awareness of pace, plus as you get into it you can start to think about your form and technique and breathing patterns.
You then do speed sessions. I call these 'red line days'. I have a stretch of lane where I live that is approx 350 metres there and back. After a warm up, I then do a 'there and back' down the lane as fast as I can and see what my pace per km is for it. Then take a short break and I repeat it for a total of 6 reps. You can then see what your fastest one was and the slowest one and the difference between the two is. It also helps to condition you to run faster, albeit for short periods than you would normally do on a run.
Finally you can do Cooper tests. Don't think of those as being just run for 12 minutes, you can bring variances into them. You can check your cruising speed by running it as I described earlier. You can do a negative interval, where you target running the second 6 minutes faster than the first, you can also do a 'redline' Cooper test where you go out hard and then try to maintain it/hang on as best you can when it starts to hurt.
Building in a combination of those things can give you some decent gains in a relatively short space of time.
Usual caveats apply relating to warm up and down properly, don't overtrain and listen to your body and build in rest days accordingly.