I mostly just bung them all together into nearest toy storage box. It bothers me (I normally love organising things), but it gets me even more down to have GroundHog Day, the same sorting out of the same toys day in, day out.
Lego is one big exception, it's too valuable to treat so casually, iyswim. Sporadically I sort some of the toy boxes properly.
Culling is a nightmare, because DD notices. She often asks about the whereabouts of items I gave to charity shop years ago (without telling her, of course). She doesn't forget and she is still fond of them.
Chief problems I have in getting DC to tidy up is "I didn't get it out", "That's not mine", "I don't care if you throw it away", "X has to help because they were playing with it too", "No I wasn't, it was Y!". If you're really strict about tidying, they will also screech hysterically at anybody who gets out their favourite toys because they're too lazy to tidy, but they don't really want me to throw it away/into the loft, etc., either. This is particularly awkward when the child being screeched at is a visiting guest.
So very often it's faster for me to sweep a space clear than try to track down the child who got the stuff out, too.