Chapter 1 of the book of Daniel covers the period when the Israelites are in Babylon due to the divine judgment for rejecting God and going after idols or paganism. They are a chosen nation. The Babylonian diet did not meet the dietary requirements of the Israelites. 

You can look at a good overview of the 10 Day Daniel fast on this web page. It is common practice for the Church to use it as a fast at times. It is basically a vegan diet. 

I personally will have a morning cup of coffee and keep eggs, along with a bit of yogurt and a measured amount of dairy in my diet. Young children, pregnant women, and breastfeeding women have different requirements. So please allow for that if that is your life situation for now. 

Some people repeat this for 40 days, making it a 40-day fast. That is a personal choice, and it is a bit longer than the traditional 10-day fast. 

Below is a 5-day menu sample, repeat twice, and you have 10 days. 

Breakfast

1. Overnight oats, oatmeal made to your liking or chia oats overnight go easy on sugar and honey. How you restrict sweeteners during your fast is your choice, as you set up your personalised Daniel Fast.
2. Toast and peanut butter with a banana or other piece of fruit 
3. Hash browns and vegetables
4. Any type of unsweetened vegan breakfast is suitable. 
5. A herbal tea-and-avocado salad combo you make could have onion and tomato tossed through it. 

Lunch 

1. A vegetable pasta soup, like minestrone 
2. Salad sandwich, takeaway, or make your own
3. Baked potato and toppings 
4. Vegetable stir fry
5. Protein shake, if that is easy, and you need something portable 

Dinner

1. Soup, you can add a bread roll if you need to 
2. Vegetarian pasta
3. A tofu stir fry with vegetables and rice.
4. Baked beans and toast
5. A vegan/vegetarian stew

Drink plenty of water and plan ahead. You will find what works for you. Be patient if this is your first time.