I think it takes a lot of time and reflecting to be able to let them know. You have to grow thick skin and be prepared for criticism. Some family members may be disgusted over it, and some may be very happy that you have found God or something that makes you happy.
From one site:
For some muslim converts telling their family of their decision is no problem at all. Some families of converts are very happy at the choice to become a muslim, and it is welcomed. Unfortunately though for other converts this is a difficult process, with various obstacles to face.
This page is designed to help new converts through this experience, or perhaps even 'old' converts who have kept their new religion hidden for some time. There is no magical answer as all families are different and will inevitably react in various ways. However, if we cannot provide exact answers, we can certainly go a long way to helping converts feel more comfortable in this situation, and by sharing with each other we will all grow stronger and more able to face problems inshaAllah.
Before we get into the possible family problems and the suggested solutions we should first emphasize that although some converts have some problems, there are many others who do not. This page is designed to help those who are met with obstacles, so may, unavoidably, come across as negative. So please remember that some families of converts are very happy that their relative has converted. Some reasons for the happy reactions are as follows:
they are happy that the relative concerned has found God.
they are happy that the relative concerned will be leading a moral life, especially in this day and age.
the family have seen the happiness that the relative concerned has found and this in turn makes them happy.
they are pleased that the relative concerned now has discipline and stability in their life.
families knowledgable about Islam, although they may not convert themselves, realise the truth about Islam (as opposed to the propaganda).
Please remember that the anticipation of telling your family about your new religion is often worse than the reality. We find that we re-run the moment over and over in our minds, imagining the worst possible outcome. Then, when we come to actually having the discussion, things go much better than expected.
Who to Tell?
When I use the word 'family' this is referring to whoever you decide. For myself, I was concerned with telling my parents and my brother about my change of religion. Telling other family members was something that to me was not as urgent, but would be necessary in time. I felt that I wanted to gain the understanding and hopefully the support of my parents prior to tackling anyone else. For others though, they may have other family members that they would want to talk to first. Perhaps an aunt who you feel is open minded and receptive to new ideas, who in fact, may help you talk with your parents. Or perhaps a brother or sister would be easier to tell initially before talking to your parents. This is just something to consider.
What Method to use to tell your family?
The actual method of telling your family really comes down to the relationship that you have with them. Have you always had a relationship that allows the free and easy discussion of any topic? Or is your relationship good, but discussions of topics that might rock the boat are rare? Or perhaps you feel you have a not so good relationship with them.
Face to Face Conversation
I would advise the best method is to just sit down and talk to them in an environment that will allow them to express their views freely, ie talk to them privately, somewhere where they and you feel comfortable. This will allow for a conversaton to take place, giving them the opportunity to ask questions and you the opportunity to get across the main points that you feel are important. I know you may feel that you want some of your muslim friends with you, but this may stifle your family's reaction, they may not feel they can ask questions about the religion in front of a muslim audience for example.
A face to face conversation also gives you the opportunity to observe their real reactions and body language, something that will be lost with a telephone call or letter.
A Letter
If you feel that you are unable to talk to your family face to face then writing a letter is an option to consider. A letter has the advantage of allowing you time to write and re-write until you are happy that you have expressed yourself in the best possible way. You have the opportunity to make sure that you include everything that you want and that the best possible wording is used.
The disadvantage is clear, you can niether see nor hear their initial reactions. The reaction that you receive will be a delayed reaction, ie when you next see your family, or when they have read and digested your letter they will phone you. A lot can be learned from witnessing their initial reaction, although some may prefer to only get a reaction once the family have had some time to contemplate what you have told them.
You might want to consider telling your family face to face, but afterwards leave them with a letter that you had previously prepared. This would ensure any points that you were not able to convey during the conversation, were not missed altogether.
A Phone Call
This method does not really apply too well to individuals who still live with their family. Going out of the house to then phone back to the house to tell them, only then to return to the house later, does not seem the best option

For those living apart from their family, this could be considered. However, if the family live relatively close by then I would suggest telling them face to face, rather than down the phone, and only consider the phone in the cases where family live at a distance and visits are few and far between.
Using the phone to tell family still involves having to talk to them, so if possible, going the extra step and telling them face to face would be better. The phone obviously stops you seeing their reaction, it is not always easy to get a true understanding of someone's real feelings down the phone. I feel that a phonecall to talk to your family about such a matter could also trivialise the issue, which is obviously highly important in your life.
However, if this is the method that you feel suits you best, then of course do it this way.
When it comes to telling other family members then a phone call or a letter could be the best option and the easiest in some cases.
Link --->
http://www.convertstoislam.com/Coping/coping.html