Cut out food gradually. You can cut out food in whatever increments you want, but I suggest you try cutting out food weekly. You can start by cutting out meat, followed by eggs, and then dairy. Of course, you can do this in whatever order and time frame that works for you. 

READ LABELS! When shopping, make sure you read labels of everything you buy. This will really help to make sure you don't buy something non-vegan. A lot of things seem like they are vegan, but when you look closely at the ingredients, there is a non-vegan item somewhere in the ingredients list.

Meal plan. Planning meals ahead works really well because you can use your menu as a guide for groceries. This especially helps so you don't get lost and confused (frazzled even) while shopping.

Eat before going out or bring a snack. In addition, this is beneficial when going out to a non-vegan friendly place, so you can eat ahead and stay on track. If you're not hungry, you won't be tempted to eat something you will regret later.

Educate yourself. Watching movies and reading vegan books is a great place to start learning. Check out my "Vegan Resources" tab for a list on the must-see/read books and movies. 

Remind yourself why you're going vegan. Remember that you're speaking up for those who can't. Remember that pain and suffering of animals goes into these tempting food items. Finally, remember how beneficial veganism is for the planet, the animals, and for your health. 

Focus on vegetables and fruits. When people go vegan, they sometimes start off by eating a lot of starches (e.g. pasta, bread, etc.), but focusing on vegetables and fruits will help you switch to eating healthier from the start and will definitely set you up for success. There is nothing wrong with pasta, bread, and other starchy things, but eating excessive amounts is something you should avoid. 

Find recipes online or use cookbooks. Sometimes, new vegans struggle with eating vegan, but by finding delicious nutritious vegan recipes on websites or in cookbooks, you will definitely never be bored. 

Make sure you eat enough calories. Calories are what power you through the day. There is a common misconception that they are bad, but this is so wrong. Fruits and veggies are naturally low in calories, but by adding beans, grains, and nuts, you will have a TON of energy. In addition to whatever physical activity you do, your body burns calories just by going through process of life (like breathing), which is called your basal metabolic rate (BMR). Because of this, make sure to fuel your body correctly.