The best way to get faster is to run faster. Sounds funny, right? Interval training is probobly the most popular way to train for getting faster. Run 1/4 mile or 1/2 mile at a faster pace than you would normally run on a fast run. If you run a certain pace for 1 hour, you can likely run at a faster pace for only a half hour. Run your intervals at a faster pace than that. You can also do tempo runs, where you vary your pace at certain times, speeding up faster than normal, slowing your pace to rest, and resuming the faster tempo, so on and so forth.
I started "jogging" because I used to play a lot sports until I was 18, then after a few years of non-activity I needed something. I used to jog in skateboard shoes holding a cd player (2007). Eventually I wanted to improve, rather than just do 3 miles everyday. Rest days became important, slowing pace to increase distance became important, and seeing the miles keep going up became important. Everything I've done in running I worked hard for. I am not someone with natural running abilities. I got to 3 consecutive months over 150 miles, completed as much as a half marathon, all at around a 10 min. pace. Slow, I know. Then i got tired of all the long hours on the road, and the eventual remark from another runner in a 5k, "Why are you running back here?"
It was time to stop jogging and start running. Shorter miles, faster times, and a lot more fun. I'm still not particularly fast, but I do what I can. I "sprained"/destroyed my ankle the first week of August and didn't run for 4 months. I just got back on the road and have run ~5 times. No issues with my ankle on the runs, but I still get the feeling that I need to get it fixed by a doctor.