One of the most important things to know in the kitchen is how to use and be comfortable with a knife. You will need to use a knife every single time that you cook so get a good one. The knife you choose to be your go to knife should be comfortable in your hand, solid, and sharp. This is similar to the one that I use.
Once you’ve selected a knife learn how to hold it. The Kitchn has a wonderful tutorial on how to hold a knife properly.
Lastly you should also learn how to care for it properly. Read the instructions that come with the knife for care, and be sure to sharpen it at least yearly, more if it becomes dull earlier. Never put it in the dishwaser and allow it to dry on a flat surface, dishwashers and standing it up in a drain can cause damage to the knife edge and tip.
Once you have a preferred knife and understand how to care for it, learning to use it is equally as important. Knowing how to execute a number of different cuts is an important part of following recipes and cooking in general. The 3 most basic cuts (chip, dice, and mince) are outlined in the photograph below. Additionally you might see matchstick, or julienne as well, but for this post we are going to stick to basics.
The type of cut is dependent on the size of the final pieces. Chopped cuts refer to large uniform pieces, with no specific size, just use your judgement. A diced cut refers to a uniform size between ¾ to ¼ of an inch. A mince is considered to be the smallest cut and should be less than 1/8th of an inch in size.
Since I am not a professional chef I thought I would add a video from a professional chef that reviews these skills. This video uses an onion, but the skills are transferable to most other vegetables.
Getting comfortable with knifes and cutting in the kitchen really comes down to practice. Even professional chefs have slip ups and cut themselves or miss-chop a carrot. The beauty of cooking is that nothing needs to be perfectly cut to taste great, just start practicing and the comfort will come in time.