When I first made the transition to vegan (from omnivore), I researched how to meet my nutritional needs and also the ethical, environmental, social, spiritual, and health aspects of veganism. I read many books, not just the popular ones, and visited blogs and websites and scholarly articles. I wanted a well rounded education lol and I wanted to be confident and understand why this was so important to me. I waited until I had been vegan about a month before telling anyone, because I wanted to be sure I could do it and was going to be ok. My partner lived with me at the time and I was already making dinners for us every night, and he didn't even notice that all our dinners were meat/dairy/egg free lol. He ate and still mostly eats his own breakfast and lunch. I am naturally a good cook and embraced the challenge of plant based cooking and food prep and substitutions etc. It is so second nature now that I am surprised when I run into a recipe that calls for eggs for pancakes for example. They are SO not needed lol.
I'm not very good at "in your face" arguing or debates, so I keep a lot of it to sharing my personal experience and how it works for me. My partner was not happy about it for a while, and it was a struggle for us. I refused to buy animal products or cook his meat and so on, with a rare few exceptions with eggs for him when he was deathly ill and could not care for himself (and doesn't like nuts/seeds much, nor fruits and most vegetables...I learned that a good sauce makes a difference.
). I showed him some short articles, magazines, studies etc about veganism, and I showed him a book about vegan nutrition so he could see that I would be able to meet my needs and be healthy. I also showed him that some UFC fighters are vegan and very successful, and that was the turning point for him lol. He LOVES UFC fighting. He is now mostly vegetarian at home and even goes entire weeks being completely vegan (until we visit his parents...sighs).
I also really thought about it from a religious angle because I have a lot of religious family and friends. I read some Christian vegan books and joined the Christian Vegetarian Association for a while so I could get support in sharing that angle to others (I am not Christian myself). It backfired for my partner's family, who think that these "Christian vegetarians" are a cult lol. So I gave up altogether trying to convince them of the ethical/moral reasons for veganism and focused on health/environment. Well, they are lifelong dairy farmers and beyond convincing, so I gave up altogether but have shared many of my vegan dishes with them since I bring all my own food when I travel there and they have been very surprised at how great vegan food is. Imagine seeing their faces light up at trying homemade hummus for the first time. Two old folks who lived their entire lives in a sheltered area of the Midwest enjoying hummus lol.
The main concern from my family and friends was that this was just another diet for me and way to control my body, because at that time I was battling an eating disorder and already mildly underweight when I went vegan. I did indeed lose about six lbs right off the bat albeit unintentionally. I worked hard to put that weight back on and it was the perfect time to experiment with all the plant based dishes out there. I made vegan pancakes, and pot pies, and a variety of desserts, and casseroles and homemade soups and breads. Food wins every time, and over time my family became much more accepting of my veganism when they saw that I was not depriving myself. In fact my mom and sister followed suit and went vegan for a while. Now they are both vegetarian for the most part. My Dad stopped drinking/consuming dairy (like me, he has a terrible intolerance to dairy/cheese etc).
So long story short, living by example in a positive and healthy manner was what helped most. I did eventually relapse fully into my eating disorder in late 2012, early 2013 and became very sick for a time, but had a health scare and wake up call and pushed hard to get back to a place of recovery, putting on 22 lbs purely as a vegan to get to a healthier place than I had been for many years. I didn't have to give up veganism to do it. It was important for me to hold to my ethical beliefs and practices, so I adjusted my diet and became more open and relaxed to trying different things like plant based "meat" and vegan commercial "cheese" and of course eating more and being ok with my body. I never promoted specific diets within the realm of veganism because that was never the focus and not as important to me. I used to be deathly afraid of fats, but I incorporate them in small amounts into my daily diet and find they give me the stamina, energy, and mental focus I need.
I always try to keep messages about animal rights and so on positive, not accusing or attacking others. I bring up concerns and remain firm in my beliefs and practices but don't attach the "murder" label to meat eaters or assume that I am so much healthier than they are. I tailor my message to each individual, much like Ledboots. I also don't waste any energy on people who clearly are not interested and can not be civil and mature about it. I'd rather educate or happily share about veganism with people who show an interest or at least are concerned with issues such as the environment, animal testing, animals used for entertainment etc. Most people are interested in the food aspects so I might share mostly about that. I also do not have to put up with obnoxiousness from others either, and I tend to not associate with those people. I have dropped friends from Facebook for this.
I've also found that strangers in real time are less likely to be obnoxious and hateful than people on line. I have leafleted and tabled for Vegan Outreach at local colleges and city streets, and people are more receptive and polite than we give them credit for. On rare occasion someone in passing made an obnoxious comment but I learned to block them out and to keep sharing with others. I also had a plan in place in case someone started to harass or threaten me, such as calling 911 or tabling near the administration office at a local college (with their permission). People do not have to agree with everything, but no one has to take abuse either. Assertiveness is very important to learn to diffuse situations and stand up for oneself without being aggressive or resorting to the same obnoxiousness.