So here goes...
Step 1: Testing waters
To assess if the person you'd like to come out to is safe or not, try asking questions, bringing them in naturally in the course of a conversation in real life or in a text (I would opt to do this face to face because it is on the whole easier to read body language than rely on nuances in text messaging, so do so only if you can't meet the person).
"What do you think of the legalisation of gay marriage in America?"
"I'm reading this blog at "agaysingaporeanchristian.blogspot.com", what do you think about gay Christians?"
Step 2: Go with the flow
This would usually lead to the person talking about any LGBT+ friends they might have and their encounters with them. Listen carefully to see how they support their friends, not necessarily affirming their choices, but just being there for them, listening to their struggles in a heteronormative society. If they don't have gay friends, that might ring some warning bells. Gay people can generally tell if someone is safe to come out to or not. But then again, give them the benefit of the doubt, and perhaps talk about other related topics to gauge their response if Step 1 wasn't enough.
"This year's Pink Dot had a record 28,000 turnout. That is amazing isn't it?"
"I know of a gay church, FCC. I heard that some of them joined because they were kicked out of their home church. It's so sad isn't it?"
Step 3: Decide whether it's safe to come out
At this point, you should know if the person is loving like God is, or judgemental like some Christians can be. It is your choice if you want to come out to the latter. I generally try not to so as to preserve the friendship or relationship I share with the person. This issue really polarises.
After having come out to quite a number of people, I generally make decisions on the fly, and if I feel God leading me. But if it's your first or second time, I would suggest you do so prayerfully.
Step 4: Come out slowly
I have never come out to anyone saying that "Hey, I'm gay." Because that is just not me. I add a bit more nuance and generally tell people I blog at this site, or that "I'm not the straightest person in the world", depending on how open I feel they are. Of course there is nothing wrong going straight for the kill, especially if you are a straightforward person. To each his/her own. So if you are like me, it would go something like this...
"I can really identify with the blogger at "agaysingaporeanchristian.blogspot.com" because I share so many experiences that she blogs about."
"It's so terrible that Christians are so unfeeling towards gay people because I can understand how they feel."
Step 5: Address any concerns/queries they might have
If you were indirect and your friend/family member was sharp enough to catch it, there will be two likely scenarios (assuming they don't yell at you because I think you've paused long enough at Step 3 to consider the implications.)
Scenario A: Your friend or family member would ask you stuff like how long have you known? Do you have a partner? What about God? And every permutation you can think of.
Scenario B: Silence.
Don't be hurt if you expected Scenario A but got B instead. Some people just don't know how to react. Don't blame them. They just need to be educated. Perhaps you can direct them to this blog?
Step 6: Heave a sigh of relief and thank God
God's with you every step of the way even if you meet with an unfriendly reaction. And ultimately, God's all you need. Although a supportive church family will definitely help, as I can attest to that.
Just remember, do not come out especially if it's not safe for you to do so. Patience is a virtue.
All in all, coming out is a rather nerve-wrecking experience for the first-timer, but it gets easier the more one does it. My prayers are with you.