My husband always opens up a piece of newspaper and cut his nails over it.
My husband puts a newspaper under his hands when he cuts his finger nails.
ーMy husband always opens up a piece of newspaper and cut his nails over it.
「夫はいつも新聞を広げてその上で爪を切る」
to open up a piece of newspaper で「新聞を広げる」
to cut one's nails で「爪を切る」
over it で「その上で」
ーMy husband puts a newspaper under his hands when he cuts his finger nails.
「夫は指の爪を切るとき、手の下に新聞を敷く」
to put a newspaper under ... で「…の下に新聞を敷く」
ご参考まで!