"He has shoes."
Translation:Tá bróga aige.
That is a common mistake that learners make at the start, and a hard aspect to break. Keep in mind that in Irish you have verb + subject + object/prepositional phrases/etc. In Irish the literal phrase is "are shoes at him". Your sentence "ta se broga aige" would be translated as "is he shoes at him" - so you have changed the subject and now speak gibberish.