Err.. What was I going to say about -- er -- basin plughole tools??? Concentrate man!
Oh yes, two screwdrivers or a pair of longnosed pliers are OK if you are fitting a new waste, but if you're trying to remove an old well-compounded waste it's very much harder and you're quite likely to twist the pliers jaws (and so ruin them), or simply not get enough grip on the two screwdrivers.
Also, these methods won't work at all (easily) on the popup type wastes that do not have a grille, only a pair of slots in the side wall.
Monument do a tool that purports to work on popup grille-less wastes (only), but it's another one of their crap designs! I've got one that lives in my not-very-useful tools bag (together with their olive cutters) because it almost always slips out of the slots when you apply force and scores the nice new chrome plate.
There does not presently seem to be a tool on the market that will do it all, but I'm working on it!
Ah yes, back to the nice photo....