Fruit and veggies:
Breakfast: Do you like yogurt? Get a large tub of plain vanilla yogurt and eat it mixed with granola and banana slices. It's a tasty and fairly cheap (especially if you replace the granola with cheerios) way to get some healthy food.
Lunch/dinner: Admittedly I am really, really, really not a healthy eater but there are always ways to sneak some vegetables and fruits into unhealthy foods to give them more substance. Put tomatoes on our grilled cheese, lettuce in your ramen noodles, eat a salad and smother it in dressing or make a simple batter and fry tomatoes, eggplant, zucchini or sweet potatoes. Make broccoli and smother it in butter. I've grown up with a mother who has reinforced the "veggies with every dinner" rule into me, so next time you have a meal, think: "What veggies could go good with this"? Do this enough and you'll get into a habit.

As for variety of foods, this is tricky. I have picky friends too who consider re-fried beans too ethnic (wtf) so I'm familiar with the fear of new foods. The HARD MODE way to do this is to go to a restaurant with a menu not in English (or bad English) and order something you don't recognize at all. However, this could be a colossal waste of money. The other thing you could do is scour the internet for recipes for a certain/favorite type of food (Japanese, Mexican, Italian) every time you're in the mood for something new. Familiarize yourself with the local asian markets and mexican stores.

Go to a store with a good fruit section. Hopefully, they'll have at least four different kinds of apples, maybe even six and up. Get one or two of each kind you haven't heard of before. Now, go home and do some taste testing.

Fruit can be really delicious, but you have to find kinds you like. There are some AMAZING varieties of apples available, but when everyone thinks "apple" they think crap like "Red Delicious" (huge misnomer). Keep an eye out for Fuji or Gala.

Also, keep a notebook with you so that you can write down interesting food things. If you're at a restaurant and you see them do something neat with pomegranates, write it down. If you're by a saladworks and something catches your eye, write it down.

OH. Salads. Don't eat boring salads (stuff like ranch on iceberg). Get yourself some spring mix, keep some toppings handy (this is where the notebook is useful), and try different dressings until you find a couple you like. Also, don't drown your salad in dressing. Put some on, mix it up, then let it sit for ten minutes. You want the dressing to soak into the ingredients.

The key to food is variety. Find new interesting things and mix it up. If you keep eating the same thing all the time you'll get sick of it quickly. Bring fruits and vegetables into your diet slowly instead of forcing it with every meal.

Learn how to make some good veggie sides.

Yellow squash is piss easy- slice it up thick and put it in a pot with a lil' water, butter, and S&P. Cook until soft. Green beans are actually best from a can imo so put some fried bacon and onion in with them greenie-beanies and simmer it as long as you can bear. Peas are awesome you should just eat them >:U delicious peas. Carrots are easy with a little brown sugar and butter; hell, just steam them a little and they turn sweet.

Fresh veggies are easier with dip, to me. Find some nice dip you want to try, and start small. I like PB the best but you might like something else- cream cheese or whatever.

Fruit is easier 'cause they're sweet; just try a ton of stuff. I discovered how much I like pineapples that way.

Chev's suggestion for a notebook is aces.