The way to link “just” to “found” is simply to skip (leave out) the “t”. The diphthongs (double vowels) can be difficult. You can practise them separately. Notice the stress is on the preposition, which may be surprising, but is very common, particularly with a phrasal verb. The final “t” is often pronounced not with the tongue, but right down in the throat, where you make a /h/ sound. This sound, which looks a bit like a question mark, is called a glottal stop.
“Find out” means “discover”, so this phrase means “I’ve just discovered/heard” some news or information.