When you arrive at Oxford go to the Bodleian Admissions Office in teh Clarendon Building on the corner of Broad St. and Catte St. The hours are Monday - Friday 9:30-16:30 and Saturday 9:30-12:30. Go up the front steps and to your right you will find the Admissions Office. Try to get there early, as it doesn't take long for a line to form.
The initial formal admission process takes about a half hour. You will need a piece of identification (a passport, etc.), a letter of introduction (if you are a student), and 10£. This will get you unlimited use for six months or 12 visits in a four year period (each visit is good for the whole day). After reading their agreement out-loud and getting your card, exit the office and turn right. Go through the courtyard, through an arch into another courtyard and turn right. There is a statud of Thomas Pembrochiae before the doors:
Go through these doors and you will be in the gift shop. Turn left and you'll see a checker at a desk. They will check your card and/or stamp it. Pass to their right, climb the stairs and enter the library (the Duke Humphrey's room is on the third floor, I believe). It is very important that you let them know ahead of time when you will be there and what you want to study, as they said getting your materials could take up to three hours (provided your order is placed Monday-Friday before 16:00).