The way that worked for me (starting from scratch with no portfolio) was to put some calls out on business groups for people who wanted free copywriting in exchange for a review/piece for my portfolio.
I’d normally advise against free work but in this case it was limited to ten customers. After that, I had a great portfolio of work, and some testimonials, which allowed me to get playing clients pretty easily (just by keeping an eye out for opportunities and even contacting businesses directly).
Eventually, I landed a full time content writing job using the same portfolio.
Obviously this is aimed at copywriting/content writing work, and so the process will (I assume) vary somewhat for different writing gigs. But I think the concept of working for free for a limited time and then utilising the hell out of your portfolio/testimonials is a pretty effective way of getting started.
Hope that helps, happy to discuss further via email (email@example.com) if you like!