“the tent of Sarah his mother.” According to Eastern custom, this could refer to the “women’s quarters” in Abraham’s tent, but that seems less likely than Sarah having her own tent like Leah did (cp. Gen. 31:33).
“and took Rebekah.” Often there was no formal marriage ceremony in these early times. The marriage had been arranged and financial arrangements had been taken care of, so Isaac simply took Rebekah as his wife and consummated the marriage. It is often taught in books on customs of the Bible that a marriage ceremony looked a certain way and had certain specific elements. Although there were certainly similarities in many cases, there were also huge differences as well, and that is especially true given the different languages and cultures, the long span of years the Bible covers between Genesis and the New Testament, and even variations in taste and feelings of what was appropriate. Isaac was 40 years old at this time (Gen. 25:20).
“after his mother’s death.” The Hebrew text is simply “after his mother,” but many English versions add “death” for clarity.