GETTING THE IDEAS ORGANIZED - This is obviously the place to start. Gaining a working knowledge about the idea, looking for vocabulary to fit the topic, finding a musical style to match the mood or setting, selecting a target audience, are there cultural elements to consider? -- these are all important elements to think about before setting out.
MELODY, RHYTHM AND LYRICS - Some composers start with the musical ideas and then turn over their outline to the lyricist to fit words to a mostly finished composition. Other composers start with words, sometimes a title or theme or a line of text for inspiration. Those few words actually drive the rhythm and melody and inspire the direction and shape of the composition. From that beginning, the rest of the piece - melody and lyrics and even arrangement and orchestration - can be created. Most songwriters work within certain standard compositional and/or poetic FORMS that have been around for centuries. The standard AABA (2 similar phrases, a contrasting section and then repeat of the 1st phrase) or the AB (verse/chorus) models are very typical song forms.
THE HOOK - New songwriters tend to forget about this element. A hook is a section of the song that packs the most punch. It is the essence of the message in the most memorable bit of melody and lyric. It is placed in a prominent portion of the song to be the most repeated and catchy part. It is the most important nugget of the entire piece. If your most catchy rhythm or melody does not present the most significant message of the song, watch out! Sometimes the entire message is lost or misrepresented because the hook actually says something unrelated or even counter to the real message of the song.
For example, I heard a song that was about the evils of overcooked vegetables to nutrition. This song was targeted to young children to try to get them to actually eat their vegetables. But the HOOK of the song came across not that "overcooked vegetables are slimy and gross," but "vegetables are slimy and gross." See the obvious problem? The catchy part of the rhythm and melody picked up only that "vegetables are slimy and gross" and what parent in their right mind wants to promote that idea to their children?
So, if you happen to be a new songwriter, be wary of your hooks! You may end up hooking a very strange and unexpected fish!