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If you're only focusing on writing as a hobby and sharing your stories with anyone who'll read them, then putting them up in your WdC portfolio should do the trick. You can also set up a free website/blog on most larger blogging sites like Wordpress.
There's no guarentee that a lot people will drop by and read them, but the stories are there for anyone who will.
If you're striving to be published or simply improving your writing, finding a writing group (possibly here on WdC) or another way of getting honest feedback is usually a good idea. That should help you spot what parts of your writing you need to work at first. No one can focus on all of the details that make up a good story all at once. Practicing is about getting to the point where you can do most of the things, like character, plot, grammar, etc., well without having to think about them. And then there's always editing. Here too, focus on one or two elements at a time.
As for getting published. There's nothing to it but submitting to editors/agents/magazines. A degree isn't really necessary unless you're striving to publish in "literary" markets, and even here it's possible to do without if your writing is good enough. The important things are improving your skills, writing the best stories you can, submitting, and accepting the tons of rejections most writers endure.