It came about at the time
This phrase is used here to mark the beginning of a new part of the story. (See: rc://en/ta/man/translate/writing-newevent)
The word "behold" alerts us to the surprise that Tamar was carrying twins, which was previously unknown.
It came about as she was giving birth
This phrase "It came about" marks an important event in the story. If your language has a way for doing this, you could consider using it here.
one put out a hand
"one of the babies put out his hand"
This is a person who helps a woman when she is giving birth to a child. See how you translated this in Genesis 35:17.
"bright red thread"
on his hand
"around his wrist"