Hi Caroline,
Best thing to do is to ask your department's ERasmus coordinator or international office for help. They can tell you which of their agreements are also for PhD students - some are just for BA/MA students. You then need to apply for one of the places and hope your coordinator picks you - it can be good therefore to pick somewhere less popular. Obviously though you've got to apply somewhere where you could do something helpful in a semester or 2 for your PhD project! The grants are very small though.
Erasmus Mundus is a bit different I think, in that it seems to be grants for masters courses that are split between several countries and they can be outside of Europe.