1. Harmony - There are a million ways to write a song in terms what harmony and chords to use. A lot of the different styles of music are generally defined by its harmony. Each type of music will have its standards as far as what harmonies, scales and chords are appropriate and which aren't. For example when writing a pop/folk/country song any basic triads (majors and minors) within any given key are all up for grabs. Some progressions are used more than others (the IV-V-I for example) but any chord in the key can be used in any combination. If you're new to songwriting, try starting with some of the tried and true before straying too far. Of course, if an interesting progression just pops out one day, just use it. Remember though, you want the song to have a strong harmonic basis so meandering through a dozen different chord progressions isn't the best idea. See this post for more about chord progressions in pop music. The biggest difference may not be the actual chords used but the application of those chords. For example Am Dm and E may be used in a pop song, a jazz standard or a metal tune but the way that the musicians use those chords will be different.
There are some instances where you would spend a lot of time going through chords and progressions and others where it isn't a consideration at all. Some music has very little as far as harmony and what does arise is a result of a basic bass line or a sound that suggests a certain harmony. In these cases the underlying harmony and chords won't be as much of a consideration. Some artists and producers spend more of their time manipulating sounds than they do thinking about which chord to play next. That said, most music we create (even 'weird' electronica, indie rock and ambient) has an underlying harmony because harmony can be defined as the layering and interaction of sounds. In the end it's best to use your ear and think about the sounds you're using. Most of the time musicians will tune sounds even though they may not be thinking about it conciously. For example it's not uncommon for producers to tune a sound up or down to make it fit better into the song. The same may go for kick drums, snares, and sounds we generally don't think as 'tuned.'
2. Lyrics - there are a million ways to go about creating lyrics for a song. Lyrics are highly dependent on the style of music; arguably more dependent than any other factor. There are conventions for good/bad/appropriate lyrics for each style of music. For example metal likes to focus on dark and disturbing images and words that usually wouldn't be appropriate for a pop song. The same goes for hip hop, folk, jazz and pretty much any style of music you can think of. What works for one, may not work for another. Dance music can get away with lyrics that don't seem to convey much of a message at all; sometimes condensing an entire song into one or two phrases. In country, folk and most rock there must be a central message or idea. In these styles lyrics are the central focus of the song and should be treated as such. Usually the better the lyric and it's ability to convey as message or feeling, the better the song. This may not apply to pop and other styles of music where the beat/melody/vibe of the song has just as much importance (or more) than the lyric.That said, apart from staying true to the style, here are some things you may want to think about when creating lyrics.
a) the social message - lyrics in certain styles from folk to rock, like to convey a specific message. This ranges from political rants to just stating a general problem with the world. You can be political in almost any style of music but some styles like folk, hip hop and some rock, it's more the rule than the exception.
b) the story - for most lyrics it's all about the story. Love is the standard theme but really it's all about the story. This usually involves universal themes such as love, loss, birth and death, coming of age, good vs evil, and living/going through life. Often it's not so much the topic (these general themes are used over and over) but in how the story is told. If it's told with great imagery and thought, the story and song connects better with the listener.
c) painting a picture - other times, the lyric is about trying to paint a picture. They don't tell a story as much as they evoke a picture or a certain emotion. Other times, it seems some writers use words, just because they like the sound of them or they sound great with the song. Let's face it, sometimes you're not sure what the hell the singer is talking about. I'm sure you can think of a couple of songs that just seem to have gibberish for a chorus.
3. All about the form - just like the lyrics, each style of music has its own conventions as far as form. Most pop/rock and country follow the Verse - Chorus - Bridge form. There are of course many variations but this is the most popular for those genres. Jazz will generally follow the 32 bar AABA form but also uses pop forms. Dance and metal have forms of their own. Dance music focuses on the build and breakdown whereas metal forms may include many different sections. It's important that you have some form in mind when writing a song. Even instrumental music follows a form be it a basic ABA form to a full on Sonata-Allegro form. It's important that you get familiar with the different forms used in your style of music so you know what your options are when putting a song together.Form will generally create an overall feeling of cohesiveness even though the listener may not be aware of it.
4. All about the style - most music we listen to uses the same basic music concepts. It's all about how you use them that makes the difference between one style of music and another. Things to keep in mind are instrumentation and also the exact sound of the instruments. There's a big difference between rock, punk and metal guitars. As there is for rock, hip hop and dance drums. Be aware of what you're trying to convey when choosing your instruments and their sounds.
5. It's in the beat - this may be self explanatory but it's something that you should put a lot of thought into even if your song isn't a dance or rock song. There are different ways of putting together a beat as well as different ways of putting together the different parts of a track. It's all about making the parts work together as much as it is working out a great drum beat. If you're got a bunch of rhythmically interesting rhythm tracks, the best beat for your track may be a simple, straight ahead beat. Music of all styles needs to breathe and move on it's own. It's easy in these days of million track DAWs to just start pileing on the tracks, but generally you're better off putting together a couple of well written rhythm parts than a million percussion tracks. Remember to let each rhythm track breathe on its own so the other parts have space to move. If you don't believe me, just take a bass track, play only on the 1 and 3. Then play a simple, short guitar chord and play it only on the 2 and 4. Leaving all of the open space lets your mind go crazy with all of the different ideas you can come up with.
6. Arrangement - this may include the ideas listed above (form, instrumentation, style) but there are also other considerations here. Key and tempo can make a huge difference in most songs and not just ones where a vocalist is involved. A dance track may drag or be rushed and then the groove may 'come alive' at the right tempo.This is true for most music. Take a song and drastically change its tempo and it seems to take on a whole new life. If you've got a dance track and the bass seems to get lost, try rising the key up a couple of semitones. The low C on that bass track may get lost but move it up to D or even C and it may sit much better. Also, you don't have to, but I usually stick to 'guitar keys' when writing rock and blues tunes. (There's nothing like the sound of the big E chord on a guitar). This also includes the way the instruments are used over the form. You would want to guitars to do something different over the verse than the chorus. You may also introduce and take away instruments throughout the different sections. These are all things to think about.
Putting It Togther
This may seem like a long list but it's really just the start. Keep in mind, it's things to think about when writing. If you're writing is getting stale or you want to try something new, take some item on this list and do something completely new. Most of the time these things go through my mind but I don't actually consciously have a list that I go through. The more writing you do, the more these things will be part of your subconscious that you incorporate without thinking. These are things that come in and out as I write and record a song. Your approach and the tools that you use are also part of this process. Finally, when you've written a couple of songs, go through some of these ideas and see if they can make your song better. Do you always use the same form, the same progressions, the same sounds? You want cohesiveness of sound but you also want to try to convey many different emotions and ideas. These are the 'little things' that may make your big ideas pop.