If you are a first time runner and are trying to run your first race of any distance, I would change my stance on what is the most important. Easy miles, slowly increased over time is the only way to build the needed base for running races. I often think of a building and the structure it needs, to with stand weather elements. If a sky scraper is going to stand tall then it MUST have a Strong Large Base! Running is the same....the stronger, larger your base is, the higher you will be able to take your running limits. With that said the number one important element in training is miles. Follow the 10% total mile increase rule and slowly build up to at least 15 miles a week for 3 months.
So now you have built a base and hopefully run a race! It is very easy to fall into a stagnant comfortable pace! The best way to increase race pace, especially for longer races is to implement tempo runs. A tempo run is a steady run of 2-6 miles run at 10k pace! Tempos train your body to sustain an uncomfortable pace for an extended amount of time...teaching you and your body that you can run faster! Just like building miles, it takes time to build up a strong tempo run. I am training for a half in June and I have run 2 tempo runs. Both started and ended with a mile warm up and cool down. My first tempo duration was 1 1/2 miles, my second one was 2 miles. If you have never run a tempo run , I suggest doing a long fartlek workout first. Which would be your warm up and cool down followed with 3-5 min. tempo paced runs, and 3 minutes of normal paced rest in between. This will help you learn to run at a faster pace. It should NOT be comfortable, but it is NOT a race. It takes running them a few times to learn what pace works. You should NOT be able to carry a conversation, but you should be able to sustain the pace for the full duration. I would rather start off a tad slower and then decide that I can increase, rather than to run too fast and have to end early or to slow down. This type of training will teach your body to use the oxygen efficiently!
I also think that it is important to find the best terrain to run on. I want to have a successful tempo run and so I try and find a route that has as little hills as possible. I am a strong believer in hill training, but not during your tempo run. Hills are just going to slow you down, and the purpose of the tempo would be a steady pace. In fact, a slight down slope is great! I personally prefer not to run them on the track. So find what works for you!
I hope this helps! I would love to have others add to this! =)