I think they're usually made with stop frame animation. Which are individual frames which alter slightly from each other so it creates a movement when it is played somewhat rapidly after one another....
Arguably the fist animate cartoon may be found in such prehistoric cave paintings where animals are painted with multiple sets of legs to portray animals in motion. There is an Egyptian mural which...
Limited to those still around on the sets- Felix The CAT, A product of the King Features Syndicate- is probably the oldest animated cartoon- dating from maybe l923 in the silent film era- there the...