There may not be a fool proof method, but there are important components to include.
Of course there is no clinical precise explanation to professional songwriting but there has been some common denominators that people hold as the general formula to writing a hit song. Here is my way of explaining those things. Of course the hardest part is actually doing it.
First and foremost you need a strong melody. That is the lyrical part of the song that is presented by way of vocals. An instrumental song will present the melody by using a solo insturment like a saxophone, guitar, trumpet, frenchhorn, clarinet, flute, piano, etc. In fact the melody is usually the part you play with your right hand on a piano.
Many times the "catchy" part of the singing is known as the "hook". Obviously this is the part you expect most people to catch on to when first hearing the song. In fact whether people love, hate or waffle in between, the goal is for people to have at least part of your song stick in their head.
Now that you have their attention and they are hooked you need to try and reel them in. Normally unless you are a musician it is the vocals that most listeners first focus in on. So aside from having a strong "hook" you need good lyrics. Now that doesn't mean they have to be a masterpeice. They just have to be catchy and somewhat to the point. It is a bonus if they contain some emotion in the message. This way the listener is identifying with your words. Picturing or reflecting on a similar experience he or she had with these same feelings.
A simple way of looking at this is like this. Picture your song as a model home set up by a contractor. They never show you an empty house. They decorate the house as if someone is living there. Then as people go through they picture their family and their life in that house. They will obviously decorate it differently but they could relate to the way the house was presented to them.
After you have the melody and lyrics polished you can concentrate on the music that will enhance or emphasize them. It is possible that you wrote the music first and put the words to your music. You still need to go over the lyrics and melody and make sure it is jumping out of the song in a inviting fashion. People should want to sing along with your song.
As for the music it can be very simple or more challenging. Regardless of the genre' the music should "match" the lyrics. Whatever tone you are setting the two should compliment one another. Remember even if you are a monster guitar player or a great drummer the average person has to be sold on the vocals, the melody first. The more complicated the arrangement the harder it is to keep in our memory as a listener.
So as unbelievable as Mozart was for instance we only hum the simpler parts of his arrangements. Same goes for say Eddie Van Halen. The average person listens to his solos and says "wow that guy can play" not "hey was that a D Dorian scale he just used?" So the musicianship is the icing on this cake.
At the same time a better musician may be better at enchancing the melody with adept phrasing or voicing. This may manifest itself in alternate chord positions or additional accompaniment. So although this too may be icing on your cake it also may change the structure of your song and improve it to a tangible degree. There have been songs rejected at first and then excepted because of something as simple as making the piano the main instrument instead of a guitar.
Finally there is production. To some extent this is a roll of the dice. You may have a great producer but he may choose a poor direction to go in. Take a song like the "Wind Beneath My Wings". That song was actually written many, many years and recorded by numerous artists before it became a hit with Bette Midler singing it. You may or may not like that particular song but the point is you see the basic components and how they were tweaked to get the right combination. I personally do not care for that song but I have heard some of the other versions and the Midler version is so much better.
Another classic example is a song written by Daryl Hall and John Oates called "Everytime You Go Away". It was on their 1980 Voices LP. However it was in 1985 that an artist named Paul Young covered the song with a slightly different arrangment and it became a hit. It reached #1 in the US and #4 in the UK. It wasn't even a single for Hall and Oates.
If you compare the two you will see an example of all that I have explained here. The original has a nice melody and lyrics that most people can relate to but the musical arrangment although it is good it is produced in a fashion that does not bring out the emotion and overall lyrics of the song. Check it out.
One day when I win a Grammy you can look back and say "hey he did know what he was talking about". For a glimpse of what I have done you can visit my page for some sample tracks from my 2002 release.
So keep writing those songs and let me know where I can hear or get your work. Let's all support the aspiring artist.