I've not been composing music very long - less than a year, at the time of writing. As a beginner, I've been using a technique which starts with the harmony, and ends with the melody. It goes something like this:
1. Decide on chord progressions. You can pick an existing format (there are plenty) or make your own - it's not hard, because there are a lot of set rules describing how chords follow each other.
2. Write a bass line. Easiest is to have the bass play the root note of each chord, and just focus on the rhythm. Still fairly easy is to make the first note of each measure play the root note of the current chord, then play other notes from the chord. You can even play notes that are not in the chord without taking too much risk, as long as they lead into a chord note. For example, the last note of the measure can be used as a non-chord note to lead back into the root note at the beginning of the next measure.
3. Write a drum track that supports the bass line. I do it this way because I find writing drum tracks harder - but you could write it first.
4. Write some accompaniment that plays the chord of each measure. Piano or guitar are typical instruments here. Play the chord once, several times, play an arpeggio, etc. All techniques work. This one should be quite quiet in the final mix, but it really helps to support the song. Sometimes I even remove it in the final mix - but it helps while composing.
5. Finally take a couple of lead instruments and write some melodies. Keep to the notes from the scale. Find small patterns you can repeat regularly with small modifications, as this keeps a sense of familiarity and continuity. Have a pattern per instrument, then change them around, or do a canon, etc.
As a beginner this approach works well - but I have a problem with it: it's the harmony that defines the melody. By the time I get to writing the melody, I'm much more constrained as to what I can say - there's already a set rhythm, and a set harmony. Yet for me melody is the heart of what I want to say with the music.
It is harder to say what you want in a very fixed format. In a way, starting with harmony is a bit like writing poetry to a strict format: you have to make your words fit a certain pattern, you have to end verses with words that rhyme, etc. As someone who also writes poetry, I know that when following such strict formats, you end up bending what you initially wanted to say in order to fit the format. Some say that's even a good thing: it breaks people out of their pattern.
My next project will have lyrics, and I've taken the approach of starting from the lyrics. Here again the melody isn't entirely free, as it's there to support the lyrics. But it's much more closely linked to what I want to say - and musically, it will be the melody that will define the harmony (I expect I will first extract harmony, then work on bass line. Rythm will be very much defined by the lyrics too I expect).
Eventually I will try starting from the melody first - and if there are any lyrics in such a project, they would support the melody, not the other way round.