If two references are required, the usual choice is your main supervisor and your external examiner, if you’ve had the viva, or a second supervisor or Graduate Tutor if not. If you need a third referee, bear in mind that it is better to ask someone who knows your work well than a “big name” who has only heard you give a seminar paper and can’t say very much about you. Unless someone invites you to send them your work so that they can read it, don’t expect referees to do this. They will already have many students of their own to support. See Getting your Work Known and Read for advice on how to extend your circle of referees. Jobs.ac.uk also gives useful advice about choosing referees.
Treat your referees with courtesy and don’t take them for granted. Always ask them, including your supervisor, if they are willing to give you a reference for any particular application, unless they have specifically told you it is not necessary to do this. Give your referees plenty of notice of the deadline. It is your responsibility to check job sites regularly so that you see advertisements in good time, not theirs to conjure up a reference in 24 hours. Send them details of the post in readily accessible form (NOT a link to a department website, which will take time to navigate); your application letter and an up-to-date CV This will enable them to tailor the reference to the particular post, which will ensure a stronger reference. When you do get a job, write to let them know and thank them for their support. You will almost certainly need to ask them again later, for a grant application or a promotion.