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Blogging is a great platform to start at. It offers you a universal "stage" where you are able to demonstrate your writing abilities, and send it out "to the world." Depending what blogging platform you use, you can find useful feedback (if you're looking for it), as well as reactions, communication and other opportunities from others who read your work.
If you're serious about publishing, I think it's important to research what kind of work you want published since it varies amongst different genres. For example, if you're looking to publish a literary novel, you wouldn't go about it the same way you'd publish a book of poetry. Or if you're submitting to an online publication, a flash fiction publication has different requirements than a fiction publication.