Ask a friend or family member to read over your work. An important first step is always to get the opinions of people close to you before you publish your work. Take any constructive criticism and channel it positively into improving your short stories until you feel confident enough to publish them.
Start a blog. Starting a blog is a simple and easy way of self publishing your work. Sites such as Blogger and Tumblr offer a free blogging service that allows you to fully customize your blog. By publishing your short stories online in the form of a blog, you can gain positive exposure for your work and can help build up a fan base.
Start your own website. Once you have become confident publishing your work online, you might decide that it is time to start your own website. Try using a service like Google sites. Here, you won't need to be familiar with technical terms to set up a simple, functioning website. If you are more serious about your writing, then you may choose to pay for a domain name and professional web hosting, which can provide a more professional style platform for your work.
Publish printed versions of your own short stories. This can be created simply in the form of fanzines and printed at home using software like Microsoft Publisher. Alternatively, you can use a print-on-demand service like Lulu, where you can print high quality copies of your short stories for relatively cheap prices.
Stay positive about your writing. If at first you don't have many people following your blog or visiting your website, stay positive. Ask friends and family to promote your work to their friends or colleagues and in time your fan base will rise.