My approach was as follows:
Went through the Java Tutorial on the Oracle website
Read 'Headfirst Java' - this is an excellent book. Its fully of cartoons and cheesy humour, but its a quick and easy read, and surprisingly effective at teaching OO concepts.
Read the Kathy and Bert study guide several times.
Took the mock exams that came with the book.
Revised by firing up a text editor and writing short programs to test myself - this was something I could do at home/on lunch break/on holidays etc. if I ran into issues I consulted the API
The study guide is excellent - the exam can test a huge range of possible scenarios and the book covers most of them.
The actual exam questions are easier than the questions in the book. The exam questions tended to be sort and focused, with no intention to trick. That said, the book teaches you to read the question carefully which is very important when answering 60 questions in 2.5 hours. It would be a pity to know a topic thoroughly but get the question wrong because you misread 'private' as 'public'. Plus, there were a small number of questions that were a bit tricky, for example used unusual casting syntax, or there was one question that did appear to be testing one topic but was testing another. I felt that about half the questions were straightforward if you knew the basics well - ie if you consistently get near 100% on the Rules Roundup Game, and the rest were of varying degrees of difficulty.
I got 2 threads questions - they were confined to the topics listed in the exam description and were not difficult.
I got no serialization questions.
The Pearson Vue software was excellent - very easy to use, and I got my result the instant I clicked finish. (Literally!)
I found I had enough time. I moved through the questions briskly enough, but answered each one. This took 2 hours, leaving me 30 minutes to go back through the full exam, which I managed with 2 minutes to spare. I arrived early for the test, but was allowed to start early, which was nice.
I'd like to thank Bert and Kathy for 2 wonderful books and to Marilyn for the Roundup game, and a variety of people who either asked or answered questions for me on this site.