Check that you have the right software for your system. If you have a PC, download Microsoft Reader. This is Microsoft's e-book reading software for Windows-based machines and it will enable you to read e-books on your desktop machine or smart-phone. Macintosh-based machines produced within the last two years already have iBooks installed or it can be downloaded. If your Mac is a little older, there are several free e-book readers that can be downloaded.
Download books from Project Gutenberg. Project Gutenberg is home for 33,000 out of copyright books, in a variety of formats. It has a lot of science fiction from classic authors such as Jules Verne and Sir Arthur Conan Doyle, including the other stories he wrote featuring Professor Challenger from "The Lost World."
Go to the Baen Books website. Based in the United States, Baen Books is the first publisher to take the unique step of making a library of free ebooks from its back catalog available. This library includes several series of books, most notably the highly popular "Miles Vorkosigan" books by Lois McMaster Bujold and the "Honor Harrington" books by David Weber.
Download small press science fiction ebooks from sites like Sci Fi Matter. This is a search engine dedicated to science fiction and fantasy and includes a page giving detailed listings for free science fiction ebooks. This includes a variety of small press publishers and authors who have made their work available for free.
Look for works by established authors. "Shadow Unit," for example, was written and created by a group of professional authors including Emma Bull, Sarah Monette and Elizabeth Bear. It follows an FBI team that deals with crimes involving humans who have been enhanced by an intelligent alien entity.