While you should still watch your grammar (or have someone proofread for you), online writing is better described as "conversation writing". Write like you would tell a story to a friend. I actually have a friend that talks to herself while working through writing a story online. In essence she is dictating to herself as she goes.
It's funny, I read mine out loud after I've written it to make sure it's easy to understand -- she does it as she's writing. There is no right or wrong, just what works for you.
At parties, in the bleachers or around the water cooler at work, we tell stories everyday. Simply start writing the stories that can be helpful to other people in some way. The internet is about helping each other by sharing our passions, experiences, successes and even failures. (I personally believe there is no such thing as a failure as long as you learn something from it.)
I have recently written 2 articles (lenses) on Squidoo that revolve around party planning. One was about a baby shower I co-hosted and the other was my daughter's sweet 16 party. In both instances, I shared what we did and made suggestions others can use when they go to planning a party for any occasion.
They didn't take much time to write but can be found by the right person searching for ideas for their particular party or shower. 93% of online activity begins with a search engine. Hopefully, my stories -- my articles -- will be indexed and displayed for those searchers.
Learn by Example
The contributors on Squidoo write their own stories as well as promoting the stories of others to help get the word out. Learn by their examples and the examples they feature.
Writing a story from personal experience, about a topic you have passion for, and publishing it to the web will help others find you too. You can be a writer -- you just have to write from the heart!