How does the ticketing system on the tube work with kids?

I'm bringing the family down to London on Saturday and I am unsure what to do on the tube with regards tickets for the kids (aged 7 & 4).  It appears that they are free so if this is the case - how does it work?

I am used to travelling on the tube as an adult, e.g. buy a ticket and use it to open the barriers on entry and exit but if you don't have a ticket for the kids what do you do?

Also, I assume I just need to purchase an off peak Travel Card for the day?

Any help you can give would be appreciated.

Thanks.