Novelist and screenwriter Elmore Leonard knew how important the reader was. More important than his English Composition teachers, that’s for sure. He never let “proper” writing get in the way of telling a great story and making it engaging for the reader.
If it sounds like writing, I rewrite it. — Elmore Leonard
Writing like you speak is harder than it might sound. For some reason, it’s easy to “put on” a tone when you start writing, without even realising it. This is something I’m still working on, and it takes a lot of practice.
It's hard not to "write" if you're just starting out as a writer. Self-consciousness is natural.
The cure? Write every day. Eventually you'll lose self-consciousness because writing has become habitual. It's just something you do, no big deal.
If you know you're "writing", pretend you're writing an email message to a close friend. That usually stops you being aware of every word, so you just say what you want to say.