"No stranger to trouble myself" means "I am quite familiar with problems and troubles". "The unhappy" means "the unhappy people", of course. He's learning to care for others, and is drawing on his own experience of misfortune to help them.

Thanks a lot! Your comment is excellent!

From the "More than You Ever Wanted to Know" Dept.: Peachey answered your question, but I was intrigued by the feminine "-a" ending on "ignara", and so a-googling I went. Apparently, Virgil puts these words in the mouth of Queen Dido talking to Aeneas. Translations vary. With that context, http://coolquotescollection.com/5963/non-ignara-mali-miseris-succurrere-disco-not-a-stranger-to-misfortune-i-know translates it as "Not a stranger to misfortune I know how to help those in trouble.", which makes more sense. And here: http://it.wikipedia.org/wiki/Non_ignara_mali,_miseris_succurrere_disco it says that "the poet wants to highlight how no one is more sensitive to the plight of others than he who has felt the same (or similar) suffering". Doesn't address your question about the English, but just thought I'd share :)