Typically you would remove the very top part of a shoot by pinching it with the end of your thumb and a finger. Try to make the cut as clean as possible rather than squash it off. You can cut the growing tips off with a pair of secateurs if you can't get the hang of it with your fingers.
I hope that it what you mean by pinching out. Now, the why! Well, take a fuchsia for example. If you buy one and just let it grow without pinching out, you will end up with a tall, leggy plant that is not bushy. But if you pinch out the growing tips regularly this will encourage more side shoots to grow and you will end up with a more bushy atrractive plant. If you want advice on specific plants, let me know which you are growing and i will let you know more.
At a rough glance only the tomatoes may need pinching out, it depends on the type. See this link for more information: