Many writers turn to self publishing after they've had a few rejections. It's important to not take rejections personally, in fact, they can actually help to improve the writers skill. To begin with, a rejection could be for many reasons. It could be that the magazine or website the article has been submitted to isn't doing anything in that specific genre at the moment.
Many websites and magazines are at least six months ahead of the current time so you're submitting ahead of schedule. Whatever the reason, don't take it personally, there are still other ways to be published.
Options in Self Publishing
There are several ways for the beginner to self publish. Many online sites will help to walk the writer through the process of self publishing. You can self publish independently or through a service. There is also an option for "print on demand" with some sites whereby someone purchases the book and it's printed when purchased. A simple search in your favorite search engine using the keywords "self publishing" will yield many options to self publish. Read the fine print and select the option that best suits your needs.
Ebooks and Websites
Additionally, you can also self publish ebooks or simply create your own website. There are also some websites that have other writers and they all publish their current books online and help each other to rate and edit the book. Again, a simple search in your favorite search engine using the keyword "Self Publish Ebooks" or "Self Publishing Websites" will yield good results for you to start with.
Enough can't be said about editing your work. You may re read the same error time and again and because you are the author, you read it as you meant it to read. Unfortunately, many great authors make this same mistake. Hire someone to read over your work and not the errors for you. Even the best of authors must take the time to do this step. It may cost you a bit, but it's well worth the effort to avoid having someone send you an email noting all of the errors in your self published book. Have them check grammar, spelling and how the sentences in the book flow. Also, make sure that if you're using a specific spelling, you don't change the spelling half way through the book. This can confuse readers and make them wonder if you're talking about the same person, or someone new. Always order a "proof" of your book before you hit the send button to send it off for print. This could make or break your book. It's amazing how many proofs you may have to go through to get every single detail the way you want it to read in your book.
Now that you know how easy it is to self publish, you likely want to get started right away. You can either upload your completed document to the site, or you can pull a template from the site and go from there depending upon the site you select to use.