The first and fundamental question you want to ask yourself is not how, but why: when your reasons are clear, the path naturally follows. I can see three strands: 1. For health reasons. This is IMO the weakest reason. I'm not interested (nor qualified) in starting an endless debate about the health risk/benefits of meat; but if you only want to eat healthier is best to start with the obvious: cut sugar, snacks, sodas…
I was pushing my parents to let me become vegan when I turned a teenager. I stopped eating meat on my 16th birthday despite their assertions that I would die. Gave up dairy a few years later, which I only ate because the dairy industry's advertising is so damn strong.
I'll turn 46 this summer, so it's been almost 30 years, and people think I'm 10-15 years younger. Teenage girls still try to pick me up. My fiance has been vegan for something like 20 years and is 40 this summer. Last year, two high school kids invited her to the prom.
And reason #5, which was the primary reason I went vegan, followed by having a sense of ethics and feeling it was wrong to enslave, torture, and murder animals, because meat is yummy: Eating rotting corpses is pretty gross when you think about it.