Fooster is one of those words much loved in Hiberno-English but largely restricted to it, not having crossed to wider dialects as galore and smithereens did.* Derived from Irish fústar /’fuːst̪ər/, and alternatively spelt foosther to approximate Irish phonology, it has a meaning more easily described in general terms than precisely pinned down.
To fooster is to fiddle around or fuss with something. It’s a kind of agitated activity: busy but commonly aimless or inefficient. You can fooster with or over something, fooster around or about, or just fooster.
Curiously, there seems to be no associated Irish verb. Niall Ó Dónaill’s Irish-English dictionary translates fústar as ‘fuss, fidgetiness’ and fústaire as a ‘fussy, fidgety person’; fústráil is the act of fussing or fidgeting, while fústrach is the adjectival form.
Sometimes fooster has slightly pejorative connotations, implying mild disapproval: a parent or teacher might give out to a child for foostering. But the word is often emotionally neutral. It has broad appeal and is used in a wide range of ways (see below); Irish culture writer John Byrne called his blog Fústar in its honour.
Since being imported into Irish English – by Sheridan Le Fanu in 1847, says the OED – fooster has been inflected per English norms, giving rise for example to the adjective foostery. Fooster itself doubles as a noun form, but the gerund foostering is more usual in my experience. There’s a strong hint of phonaesthesia about all of these.