The kid in the first image seems old enough to begin using a computer, though you would probably start the kid off with an older laptop, or possibly a cheap netbook so that if they damage it, you are not out a ton of money.
At the ages of 0-2 they can learn the basics of controlling the system (launching applications, using various input devices (mouse, keyboard, touchpad, touchscreen). They can then occupy their own time by doing basic things such as watching cartoons and movies. At age 2-3, they can then use their better understanding of language to take a more active role in using the internet and learning how to keep their system secure. Once they understand the basics of security, then by around 5 years old, they will likely not need any supervision from an adult since you can more easily trust them to not install a ton of malware.
Between the ages of 3 and 5, you may also want to have your kid learn to build a PC and perform basic maintenance. This will not only allow them to be more mindful for the components and more caring in their treatment, but it will also improve their thinking process in solving problems.