As a general employment rule of thumb, if you don't understand the training you were given, then you weren't given the right training.
But it sounds like this is an informal handover of roles between employees, rather than a formal training process.
If you think you need detailed learner-specific instruction, then you ought to approach your HR department (they will probably have a formal job description relating to your new role, which will usually contain such vital but often-overlooked details such as: Description of the precise duties you are expected to fulfil, who your key contacts are, etc. etc).
If you are 'out' to your predecessor (or choose to come out to her) then she might be a bit more sympathetic on a personal level for a while. I'm not sure how accessible she will be in the future (you say she's leaving the company), but would she (for example) mind if you rang her on her mobile for guidance if things go drastically wrong?
Failing that possibility, you should approach the two supervisors you have labelled X and Y and explain your information-processing needs (ideally with a constructive suggestion or two up your sleeve, about how best to communicate and prioritise instructions).
Or you could just dive in head first, make loads of mistakes while you're still learning the ropes, learn from all your experience (good and bad), keep your head down, laugh at the boss's jokes, make coffee regularly and eventually perhaps figure out your own individual way of doing the job.