When you first convert to Islam, one of the most difficult thing you have to deal with is the reaction of your friends and family to your conversion. Your parents have raised you in one religion or way of life and now you have chosen another way. Their reaction will depend a lot on their world view: their religion, your community, the strength of their own faith (or if they are secular), their impression of Islam…
I must say when I converted I handled it quite badly. As my parents were religious, I knew it would hurt them, so initially I tried to hide my faith from them. In the long run this was a big mistake, as they saw it that I was being dishonest rather than trying to protect them. The shock of my conversion was just as great, but they missed the gradual process that lead me to Islam. I also launched into debates about Islam and Christianity that neither convinced them about Islam or helped the relationship between my parents. Other problems I’ve heard converts make is becoming very extreme or arrogant or getting married immediately after conversion ( Of course getting married is a good thing, but take time to know about Islam and for your family to understand you are Muslim or they may think you just converted for marriage).
At the end of the day, how you handle your family and friends it's going to be your decision based on the understanding of your circumstances. You may lose some friends, family may turn against you. But the best policy is honesty. Even though there is going to be some reaction initially, remember it is going to die down. The crucial element in this strategy will be your good, intelligent behavior. Tell them that despite your change in faith you are still their son or daughter. There is a natural bond between parents and their children which is special in Islam. Muslims are required to keep the ties of the womb. In fact, severing the ties of kinship is one of the major sins in Islam. For this reason, Muslims exert a lot of effort to visit their family and relatives and always try to avoid contention and bad feelings that may result in severing ties.
You owe them even more respect and attention in Islam. Arguments tend to drive people apart and entrench opinions so don't unnecessarily preach to them if they get irritated; just create a good example and be patient.
Our lives are in the hands of Allah. We should do our bit as best as we can; He is most certainly going to do His.
The following advice comes from website called readingIslam.com (I’m not promoting the site, but I think it has some good advice on this topic and wanted to acknowledge the source):
Upon accepting Islam a new balance has to be struck so that the new Muslims can maintain their identity and principles while at the same time showing compassion, kindness, and good treatment to non-Muslim relatives who may at times be critical, negative, and even abusive. Keeping the following points in mind may be helpful:
• The Prophet was always humble. It's very important that Muslims don't feel superior to others. We do not know if Allah will accept our deeds. We never know who He will guide to Islam. If we can be humble, yet assertive with our non-Muslim family members, we have a greater chance of touching their hearts and letting them see the practical goodness of one who adheres to Islam.
• Always be polite. The Prophet never caused dissension between people and was never a part of such behavior. He always accepted invitations (as long as the activities were in accordance with Islam) and he never refused a present no matter how small it might have been.
• The Prophet was always cheerful and smiled pleasantly to everyone. Anyone who was with the Prophet thought he liked him the most. We should try to be like that with our families.
• We should always show mercy. Allah says what means [ And We have not sent you but as a mercy to the worlds] (Al-Anbiyaa' 21:107); and [Thus it is due to mercy from Allah that you deal with them gently, and had you been rough, hard hearted, they would certainly have dispersed from around you; pardon them therefore and ask pardon for them, and take counsel with them in the affair; so when you have decided, then place your trust in Allah; surely Allah loves those who trust] (Aal `Imran 3:159). Showing mercy, even toward those who are harsh with you has a very positive affect on the heart and soul and may turn that hard heart into a soft heart filled with light.
We are blessed by Allah according to the patience, forbearance, and sincerity we show in the midst of difficulty. The new Muslim faces many challenges but these can be seen as opportunities to grow and gain reward from Allah. An internal conflict arises when you are trying to turn away from old habits and practices and adopt new and better ones and yet find yourself surrounded by people who are continuing in the old behavior. It is necessary to balance between regulating your own behavior and yet allowing those around you, even those closest to you, the freedom that Islam prescribes to act according to their beliefs. As long as their beliefs do not encroach on your rights, it is a matter of life and let live.
Allah says what means in the Qur'an
[Say:, I worship not that which you worship,
Nor will you worship that which I worship.
And I shall not worship that which you are worshiping.
Nor will you worship that which I worship.
To you be your religion, and to me my religion.] (Al-Kafirun 109:1-6)
• This kind of freedom gives everyone the space to think, ponder, speak, and act but without being aggressive. So if, for example, you attend an event that is a strong tradition in your family, you are free to calmly and kindly say that you won't drink alcohol or sit at a table that has it, that you will stay to greet your family, but won't indulge in inappropriate mixing of the sexes and so on.
• By establishing your boundaries and calmly explaining why these principles and values are so important to you, you are spreading the message of Islam and keeping those family ties intact.
• At first some people may ridicule, scoff, object, or even confront you, but just keep in mind the principle of freedom that every person acknowledges the value of, and simply say that you are exercising your freedom and allowing them theirs.