A few things that worked with my coming out, especially my difficult ones:
1) Knowledge is power. Knowing about gender identity and dysphoria can help you start laying the ground work for the coming out. I started by asking both my mum and my dad if they knew what the terms meant, and then explained them. Knowing what you are going to go through in transition, the steps and processes involved, can help you put their minds in at ease. You know about this stuff, have been thinking about it for a while, but to them it's new and scary. You can help them get past fear with your knowledge.
2) Stick to your guns. You aren't negotiating. The people you come out to will probably try and push back on something. The course of your treatment, when you come out to friends and relations, what your name should be... there will likely be a sticking point. You can't give in, because this is about you and your desire to be yourself. It isn't something to be compromised. You can listen to and even take their advice if it suits you, but you have to be in control of this.
3) Your identity is not up for debate. Denial and gaslighting seem to be common reactions, especially among close relationships. To protect they "you" they have come to know and love, they will try a number of tactics to get you to question your identity or your desire to transition. Being trans is something that cis people can only understand in the most abstract way possible. They can't feel what you feel, and they only have limited examples culled from media and limited contact, so they'll try to either fit you in those boxes or say how you can't fit in those boxes. Don't buy into it, and recognize it for what it is, fear and grief.
4) Let the fear and grief run its course. This is the hardest part in my estimation. Sticking to your guns about your decisions and your identity, knowing what you want, these are easy. But as they can't understand what you're going through, you can't quite understand what they're going through. There may be hurtful things said, tears and recriminations, and times where it feels like the relationship might break. I suggest not letting this happen. Now, if you're in emotional or physical danger, that's one thing... but if you can and want to take the storm, it's worth it on the other side.
5) This is more of a long term thing, rather than a tip for coming out, but show people that your life has improved. All of the people I've come out to have commented on how much happier I seem, and that helps them cope. Give your loved ones the same gift, if you can.