Walaikum Asalam,
Welcome to Islam! And thank you for asking such an important question.
I understand that this is a very sensitive topic to broach with family. They may feel betrayed by your choice to seek a different religion from the one that perhaps they spent so much time educating you and raising you in. But you can be patient and gentle with them and explain to them why you have become a Muslim.
Now, before you break the news, you need to take into consideration what your family’s current views of Islam are. If they have very negative views of Islam and Muslims, it might take a bit more time and finesse. First, you can start to tell them by showing. That is, you should start treating them as a Muslim should treat his or her family. This means being respectful and helpful no matter how they treat you.
Show them Islam first. Then you can start talking about the things you have learned about Islam as a way of more directly showing Islam to them in a positive light. Then, after some time of doing both of these things, you can tell them you have become Muslim yourself. These steps might help soften the blow they might feel from this news.
You can ask them kindly if they would give you the respect of hearing you out so that you can explain why you have chosen Islam. If they are too upset, then give them space. Be kind to them. Change is hard. And your converting might be a big change for them.
If you get upset and storm out, then you are closing doors you do not want to close, and Allah (SWT) directs you to never close. Allah (SWT) instructs us to never ever cut off ties with our family. So, try to see things from their side and bring them little by little to a better understanding of Islam and why you chose it for your life.
If you broach the topic of Islam and find their views aren’t so negative, then still have wisdom and show them kindness, always. But maybe you won’t need to take it as slowly.
Here is a letter I have written to the families of new Muslims that might help you broach the topic with them. Maybe you can even email it to them when you are ready. There is no real rush. And here is an article my sister wrote about how she felt about my conversion, how we are still sisters and best friends, and that there was nothing to fear. I hope this helps. May Allah (SWT) make your path easy.
Views expressed by hosts/guests on this program (live dialogue, Facebook sessions, etc.) are their own and their appearance on the program does not imply an endorsement of them or any entity they represent.