Hi Aidan_Kierans,
In the three cases I know, it went like this:
CWI: the student got in contact with a researcher from CWI who was willing to supervise a thesis.
CHAI: Same.
Mila: Same.
Note that for CHAI and Mila, you may need recommendation letters if you go over their usual routes of research internships. I myself also applied to Mila and FHI and got recommendation letters for this, though in the end I was not able to get accepted there.
The programs in continental Europe (e.g. Amsterdam, Darmstadt, Tübingen, ETH, and Lausanne) are usually 2 years long and the UK ones (Edinburgh, Oxford, Cambridge, and UCL) take one year. I don’t know how well the UK ones adapted their program to online teaching, I have just heard that Edinburgh is currently struggling to do so.