We do get some help from the government, but after paying the rent, there really isn't much money left.
"We do get some help from the government"=「私達は、政府から少しは援助をもらえます」
("some help"を"some assistance"と入れ替えても良いです。"help"よりも"assistance"の方がフォーマルな言い方です)
"but after paying the rent"=「でも、家賃を払ったら」
"there really isn't much money left"=「あまりお金は残りません」