YouCompleteMe doesn't introduce a lot of new key bindings, which makes integrating it into your workflow easier. Enter insert mode and start typing away:
As you do, autocomplete suggestions will pop up. The Tab key will cycle through suggestions. Furthermore, if YouCompleteMe is able to look up function definition, together with a supporting docstring, it will show up in a preview window at the top of the screen:
The preview window only shows up when YouCompleteMe uses the semantic autocomplete engine. The semantic engine is automatically invoked after typing . (period) in insert mode or manually by pressing Ctrl + spacebar.
For Python, YouCompleteMe also allows you to jump to function definition. Add the following mapping to your .vimrc file:
noremap <leader>] :YcmCompleter GoTo<cr>
Now, with the cursor over a function call, press your leader key (backslash () by default), followed by ]. You will be taken to the function definition:
YouCompleteMe is not the only available autocomplete tool, but merely the author's favorite (and the most popular option at the time of writing this book). There are many alternatives. A quick search along the lines of Vim autocomplete will yield plenty of results if you're interested in an alternative.