What makes Fukuoka's local dialect, Hakata-ben, different from standard Japanese? The single part of speech that symbolizes Hakata-ben for most people is the word {ttai{ (or sometimes just {tai{). This is a suffix that is added to the end of sentences, and generally is used almost the same as {yo{, to tell the listener that this is new information. An example:
English: The Hawks (Fukuoka's local baseball team) won again today.
Standard Japanese: Kyou, Hookusu ga mata katta yo.
(Direct translation: Today, Hawks [subject] again won [new info marker].
Hakata-ben: Kyou, Hookusu ga mata kattattai.

There are of course small differences between {ttai{ and {yo{. {ttai{ sounds as if the story will continue afterwards, more so than {yo{, so if you stop talking after saying {ttai{, there's a good chance the other person will say {sore de?{ ({and...?{), expecting you to continue.

Just by adding this to the end of your sentences, you're halfway to sounding like a born-and-bred Fukuoka native!