This is a very big concern these days and is a topic I am often asked about - and as a parent, it is a subject of great concern. It is a topic that raises many questions of how, when, why...... and is also an area that is often overlooked by many.
Do not overlook other devices
Before reading further or dismissing altogether take a moment to consider that much of this applies to not only computers and laptops but to any other internet capable device such as a tablet or smart-phone etc.
Access for all ages
As adults we have to understand and respect the fact that the Internet is pretty much open-plan by design and is a valuable resource with the ability to be able to browse almost anything. The flip-side to this is there is also the ability to see much we actually don't want to see! Whether the Internet be restricted is not for discussion here but more the point of understanding the options available to restrict or prevent access to certain parts of the Internet or its functions e.g. in the home you could perhaps have age-related restrictions in place that could block or prevent access to certain websites or functions allowing the freedom to browse unaccompanied.
The best approach?
There is no definitive answer to this and much is in the hands of parents to determine as to what level of access they want children to have - some go for the open access 'no restriction' approach, others go for 'not unless I'm with you' accompanied approach whilst others may not even have considered this at all... and the latter is very much a concern. Whilst you may be able to trust your younger ones, bear in mind that the web is a big place - and an inadvertent click or the chance of temptation may result in something considered inappropriate.
The best answer?
The best answer I feel is just to be aware i.e. have a general understanding and awareness of the internet, the risks, security, what is out there and what may or may not be available to access from particular devices or by certain users. Make sure your devices are protected to help fight and prevent viruses and other malicious stuff that may be inadvertently be downloaded. Be aware that there are ways of restricting access or content deemed inappropriate.
There is also plenty of software available that handles much of the technical details in order to provide appropriate access levels by way of user age or type and is relatively easy to control. Such software can give additional reassurance and provide a safer environment for family Internet use.
Just be sensible
(As ever) if I can be of help then give me a call.