How do they check a contact less debit card on the tube or trams?
A Revenue Inspection Device (RID) is used, which is capable of checking Oyster, ITSO smartcards, Apple Pay and contactless cards. The only check approved for contactless cards is to see if they are on the Not Authorised For Travel list, which is periodically downloaded onto the RID via 3G; if the card isn't on the list, it is approved by the device when it scans the card, and that's all that the member of staff knows.
More detail is provided when using the RID to read smartcards and Oysters, although the PAYG balance cannot be shown for Oyster cards.
It must be said that only the more "clued up" TOCs issue RIDs to their staff; there are some locations where operators haven't got round to training their staff and issuing them to all (or any) depots.
Depnds on the TOC, on Southeastern tickets are checked every journey however on Southern its extremely rare. Southern should perhaps look at employing even tempoary revenue inspectors to give a bit of staff visibility. Seems to me a lot of the on board staff really can't be bothered.
Southeastern definitely don't check tickets on every journey, but their guards are generally pretty good on the mainline routes.
In terms of the DOO London services, they have roving REOs (Rail Enforcement Officers), who are probably above and beyond anything else provided by TOCs on the national network in terms of enforcement coverage and professionalism, and you do tend to find them supporting a fair number of revenue "blocks" on targeted trains and stations in the London area. But not everywhere!
As for GTR, expect a lot more action against ticketless travel soon.
On the DLR they have a device which reads the card and presumably confirms that it has been touched in. Not sure how though.
As above, that's a RID. It doesn't confirm if a card has been touched in; revenue staff are not permitted to track the usage of contactless cards, only see whether it is authorised for travel or not.