Identify a research area you wish to study. Unlike undergraduate, or even taught postgraduate degrees, you will need to carry out your own research, ideally in an area that has not already been subjected to academic study. Identifying a gap in existing knowledge and then putting forward a successful pitch as to why this needs to be addressed and why you're the person to do it, is the first step of undertaking a Ph.D.
Decide on your institution. It may be the case that you can continue on at the university where you studied as an undergraduate, or the one nearest to you, but this is not always possible. The biggest factor is often whether or not there is a suitably-qualified professor willing and able to serve as your supervisor. So, look into the research interests of academic staff at various institutions, send off some speculative e-mails and find the university that is right for you.
Check the academic requirements for a Ph.D. program. Even if you have identified an area of research and found a professor willing to supervise your studies, you still need to be accepted by the university in question. In many cases, schools will ask for a master's degree but this is not always the case. A good bachelor's degree, coupled with excellent references, can be enough to get you into a Ph.D. program, though you may be asked to take classes in your first year and build up enough credits for a master's.
Secure funding for your studies, if at all possible. Some Ph.D. programs are offered like jobs with fixed salaries and responsibilities. Be aware that competition for them is extremely tough. Alternatively, apply for a grants, loans or a combination of both with these often advertised in university departments or specialist publications such as science journals. It can be possible to fund a Ph.D. yourself, though this may mean you have to study part-time or teach in your department.
Study efficiently. Simply putting in the hours is often not enough to progress with your studies. You have to work smartly as well as hard. So, break your research down into manageable chunks, setting strict goals and deadlines and try not to get waylaid by irrelevant information. Keeping on top of your bibliography and sourcing from the start -- for example, by using programs, such as Endnote -- can save a lot of time and hassle in the long run.
Work along side your supervisor or supervisors. Though Ph.D. students should not be "taught," you should be able to benefit from regular meetings within your department, so make use of them. As well as giving you tips and steering you in the right direction, supervisors can also keep up your motivational levels and keep you informed of the latest developments in your study area.
Keep motivated. A Ph.D. can take up to four years, during which time you need to stay focused and motivated. Becoming an active member of your department and getting to know fellow Ph.D. students can be a good means of staying motivated, while adopting a "9-5" working day is also good for self-discipline. That said, be wary of burning yourself out. Don't let your studies dominate your life, but rather enjoy a balanced lifestyle, with this likely to help your mind stay fresh and positive.
Write your thesis. The vast majority of Ph.D. programs call on students to submit a final thesis of original work by a set deadline, usually three of four years after a study start-date. The important word here is "original." Plagiarism is a big deal and can lead to an automatic failure.
Defend your thesis. As well as submitting the thesis, Ph.D. candidates are often required to complete an oral examination in front of a supervisory committee made up of experts in their field. Be aware that these can sometimes be open to the public and the panel can be brutal in their breaking-down of your work. However, once you have passed this final hurdle, you will have obtained your Ph.D.