Free to air means that you don't have to pay a subscription to receive particular channels. In the UK only the BBC channels, ITV channels, Ch4, Ch5 and a few Freeview channels are classed as Free to air.
Freeview is the digital terrestrial television service in the UK. Not all of the channels are free, there are more 'subscription' and pay-to-view channels arriving on this platform.
Freeview HD will need a special HD box but the HD channels are at no extra cost.
Freesat is the digital subscription-free satellite service for the UK. It does not carry exactly the same programme set as Freeview. But once you have bought the dish and receiver there are no other charges.
Freesat HD will need a special HD box but the HD channels are at no extra cost.
Sky and Virgin are all-subscription platforms. They carry the widest range of channels and some of these require an addition payment on top of the basic service charge.
Sky and Virgin HD need a special box and they charge extra to use it (and extra £10/month for Sky), plus the cost of any HD programmes. Personally I think Sky is a rip-off.
Whatever "platform" you choose as your source of television you will still need a tv licence. This is required by the government as permission to own and operate a tv receiver.