Kovid's solution works by leaving Calibre running all the time and making it accessble to the Internet via your Internet router, dyndns, etc. The advantage is you get all the features of the content server.
The Dropbox solution isn't as feature rich, but it has the advantage of not requiring Calibre running or setting up an Internet available service yourself.
Dropbox (and Sugarsync, and several other players) provide free Internet storage space, generally up to two gigabytes. That's plenty for most ebook libraries. All you do is sign up for their service, then install their client software. The client software works in the background to sync specific folders on your desktop to the Internet. Specify your Calibre library and it will automatically sync to the cloud whenever you add/change books.
The second piece of the puzzle is Calibre2OPDS. This indexes your Calibre library and builds an iPhone/Android friendly UI to browse your ebooks. You need to manually run this whenever you change your library and you want to update the web index.
Then you either configure Aldiko to use your dropbox account as a catalog, or just browse the catalog directly in the Android browser-Aldiko will be launched automatically whenever you download an epub.
Read more here:
https://www.mobileread.com/forums/showthread.php?t=64095