Just a question for clarification. By your phrasing, I assume that you aren't asking only about immediate-blood relations (sibling-sibling; parent-child), but also about close relations such as first- or second-cousin marriages, yes?
On a side question. If it wasn't that common, how was it explained to commoners when Royals did it? Was it common knowledge or was it hidden from them?
There is a long history of regulating relations between close family members in order to prevent inbreeding. In England, these rules are still in force. First laid out in the Book of Common Prayer in 1583, the Table of Kindred and Affinity prohibited marriage between family members linked by blood. This was progressively further expanded to in-laws of close family members by blood, although this was only instilled in successive iterations of the laws regarding incest. You therefore had a series of odd relationships, especially amongst the English and Welsh gentry, that might shock us today.
If you were looking to start a family, you could never marry your sister or your brother. You could not, likewise, marry your aunt or uncle, your mother or father, stepchildren or your children-in-law. Obviously, you also couldn't marry your grandparents, but that would be remarkably icky to begin with even for the pre-reformation Tudors.
So who could you marry? Anyone unrelated to you was fine. However, first cousins were considered to be unrelated. Bizarrely, you could also marry your step-siblings although I imagine this was extraordinarily rare and I imagine a rector or curate would probably refuse them the rites of marriage. You could marry your brother's fiancé although this was relatively rare after Henry VIII fell out with Catherine of Aragon for this precise reason. Interestingly, George V did marry Mary of Teck, his older brother's fiancé, in 1893.