It gets easier every year to publish a book. I published my book on Kindle Direct Publishing. It is fast, free, and easy to use. Nook also has PubIt. PubIt is also a direct publisher.
Try CreateSpace if you want your book to be available as an actual book. They also have really good marketing packages that include:posters, bookmarks, and several other things. They charge around $3,000 to $5,000 to distribute your book. If you don't want to mass produce, you can also order individual copies of your book(s) for friends and family.
If you want to show off your book for free and not get it really published, try Booksie. There are tons of users that are willing to read your book. Even though you won't actually be published it would be a good idea to post your first book there.
An idea: Put your first book out on Booksie for anyone to read. When you write your second, publish it to createspace or Kindle Direct Publishing so you already will have a fanbase willing to read your book.