How does Geany auto-completion wơrk?

How about simply put: Ctrl+Space

I know 4 years passed ... but the correct answer is :

Edit->Preferences->Editor->Completions->[Check the "Autocomplete all words in document"] press (CTRL+SPACE)

Geany does have autocomplete.

The main way autocomplete is used is by typing a long word, and by narrowing that list of autocomplete possibilities down. Let's say you type gtk_combo_box_. It will have a small list of different commands that match this description. Typing eTAB will narrow the search down to gtk_combo_box_entry_. Typing sENTER will then bring it to the proper to gtk_combo_entry_set_text_column. See the Geany manual.