different for every person.
some people work better at quitting things cold tofurky. Others need a more gruadual approach.
I myself went cold turkey. I find it easier for me to set a boundry that cannot be crossed. Because if I gradualy try to do something, I just won't do it. Example: "oh theres just a little cheese here, little egg here, it wont hurt" or thinking that since I havent actualy "went vegan" yet, I can just get that cheesy pizza tonight.
I find it easier to just set a boundry and stick to it right from the start. One night I made the decision to go vegan, and that was that.
Some people handle gradual things better.
It really depends on your own psychological make up, and how your mind deals with these kind of situations. Have you ever had a lifestyle change in the past? Did a certain way work better for you?
Also, when I get cravings for those things, what should I do?
Suck it up and deal with them... Honestly you will get cravings, especialy dairy, cause dairy is addicting. But if you get through your withdrawl stage they wont be so bad anymore. Besides that you can find replacements for certain sweets and stuff. There are vegan granola bars, vegan chocolate, vegan cookies and baked goods. If you have a Whole Foods or Trader Joes near you it would help tremendously.
The biggest thing to keep in mind is why you are doing this. Remind yourself. When you get a craving, or think about eating something, remind yourself why.
Cravings will pass. I've seen people say "I wish I never ate that pizza, I was doing so good, 3 weeks without dairy and I just threw it all away" but Ive never seen anyone say "I wish I would have caved into my cravings earlier".
Cravings will pass, withdrawl will pass, regret lasts a little longer. And thats true with any goal you set for yourself.