When the news comes out that your daughter is gay, the best thing you can do as a parent is to be as supportive as possible. You can’t make it about you and you can’t make them uncomfortable. It took a lot of courage, guts, and strength for them to do what they did. Because of this, you need to stay in their corner, let them know you love them, and that this does not change the way you look at them. You love them just the same. It might be a shocker at first or you might have known all along. However, it is up to them to decide when to come out and on their terms.
As a parent, you cannot judge them, think of them differently, or make them uncomfortable. The key is to listen to them and let them get everything off their chest. Chances are they have been holding this in for a while, but they were waiting for the right time to come out. They have not felt comfortable or at ease about it. When they finally do it, it is up to you to make them feel at ease and like they can talk to you about it. The last thing you want to do is alienate them from you.
Now, with things like this in life, people are going to react in a variety of ways. Not everyone is going to accept it, understand it, or like it. However, as the parent, it is up to you to let them know they are loved unconditionally and nothing is going to change in that regard. If anything, you will love them even more as you will have a better understanding of who they are and what makes them tick. For the time being, it is best to not ask them too many questions or overwhelm them.
When they are ready and they feel comfortable that is when they will tell you what is going on with them, how they feel, and how they came to this conclusion. You have to treat it like business as usual. It is a big milestone, yes, but chances are they do not want a lot of attention surrounding it. They want to keep it as low-key as possible for themselves. Once they feel fully comfortable in their skin, there will be backlash. In the end, it will make them stronger people.
You also have to understand this does not change the fact they are your daughter. If you are old fashioned, you are going to have to get used to the fact that some girls are going to be coming over to date your daughter and they might kiss. You have to know that times are changing and it is important that you adapt and change with them as well. You have to keep a positive attitude, a supportive one, as mentioned, and make this as painless as possible for them, so they can embrace being the best version of themselves.