There are several methods they used, a few of which, are still used today.
Method 1: Put on a "straight" public appearance, marry a "beard" and have kids that way, but live a secret double life with your lover in a place your regular family and friends don't know about. (This one isn't as common anymore in Western culture, but is still done in other parts of the world).
Method 2: Lesbian couple wants to have kids, so one of them pretties herself up, goes to bars, and gets knocked up. (Still done today if they can't afford artificial means).
Method 3: Gay couple wants to have kids, and one of their lesbian friends offers to carry a child for them. (Still done today).
Method 4: Adopt (though that only became legal within the last couple of decades).
Now from a historical perspective, there weren't as many LGBT people around in times past, partially due to their lifestyle being taboo in regular society, and lack of communication. Most of the time, they had to keep their orientation a secret, or lose everything, maybe even be executed. They typically hid themselves in plain sight. What LGBT people who did exist either used Method 1, or did not marry or have kids at all. But they did not die out.
The more interesting information came from European royals and nobles who were gay. Their status mostly protected them from the wrath of the Church, but they still carried out their LGBT activities in secret. The court could whisper and gossip, or snicker, but they weren't allowed to openly diss the monarch or royal relative, particularly if they were high on the food chain. The few gay royals and nobles who did exist often had to put their orientation aside in order to do their duty and have heirs, otherwise their family line would die out and their fortune/country/status would be lost to someone else upon their death. Therefore, it was pretty normal for them to have legal marriages to the "right" people, get pregnant and have at least one surviving heir, and then go off to do what they wanted in private. For once, arranged marriages worked in their favor.
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