It depends on the specific language and how its features match or mismatch your strengths and weaknesses as a learner, for instance:
- for mandarin Chinese I started by listening intensively because I am very bad at distinguishing tones and, in general, sounds are very different from my mother tongue, same thing for English. Didn't study Hanzi because was busy with Kanji (for completeness: had to give up mandarin after completing Pimsleur 1 2 and 3. for the time being)
- Japanese I started studying only the writing system because pronunciation is very similar to Italian
- Spanish I would start just by reading, pronunciation regular and reasonably similar to my mother, many words are similar
- French I learned mostly by listening because grammar is very similar to Italian and because at the time I was too busy with work and had no time and energies for grammar :-)