In many vocal traditions (such as the Barbershop Quartet) it's pretty common to have the melody switch between parts, so one part won't necessarily always have the melody.
The melody itself tends to be made up largely of chord tones, and if not suspensions and passing tones which don't really sound that dissonant in context as the ear hears where the melody is heading to. Certainly the melody will double one of the other parts at times but often all 4 parts will be describing a chord (such as 1, 3, 5 and 7). Beyond getting the melody and harmony in place there are many other considerations, such as avoiding parallel 5ths (unless using them for a deliberate effect) and getting contrary motion between the outside parts.
To do this really well, study baroque counterpoint. There are tons of books on this and most of the examples tend to be written out in four parts. Modern four part writing is based on this.
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