There are lots of different ways to find funding for a PhD programme. In this post, I'm hoping to illuminate a few of those options for you as well as tell you how I got funding for my PhD. There's probably many more options out there than what I'll cover, but if you're at the point of considering a PhD, perhaps this might be helpful to you.
A lot of your funding options will depend on what you want to do as your project. You might not have a specific idea in mind, instead you could have an area of interest. If you're still an undergraduate, I'd always recommend speaking to lecturers you know who teach in that area - not only is it a great way to bounce around ideas, but they might know of people in the field who you may be able to apply to work with. Failing that, you could try browsing projects already available at Find A PhD; there's forums there too where you can discuss various aspects of a PhD.
There are several scholarships you can apply for - in the process of my attempts to get funding I applied to three. Those were EPSRC, ESRC and Carnegie Scholarship. You can find out more about those on their respective websites (easily found through Google). Again, it's up to you and how you want to conduct your research that will indicate which might be better for you. ESRC offers what's called 1+3 funding, where they fund you to do a one year Masters before your three year PhD. EPSRC and Carnegie only offer 3 year funding (PhD only). I also learned that due to the economic climate, ESRC have changed how they fund PhDs. Now only certain universities can apply for funding from them, so if you are applying through a specific university, you may want to check with your supervisor/the website to see whether ESRC still offers funding to your institution.
Sometimes, if you're lucky, the university you want to apply to will have in-house funding. These may be called studentships, or demonstratorships, and often involve a teaching componant in exchange for a fee waiver and stipend. Obviously, everyone is trying to make cuts at the moment, which is why you're particularly lucky if your university has some. I was one of those lucky people, thankfully!
The actual application process for all these methods are different. For Carnegie, EPSRC and ESRC, you fill in a form with your personal details, some information about your experiences, your proposal (normally no more than 500 words) and two references. Once you've submitted the form, it's all out of your control and you simply have to wait for an answer. University studentships are usually more rigorous, as teaching is involved and the staff must ensure you are capable of upholding the duties required of you. For my studentship position, I was required to submit an application and then go through an interview panel.
The interview itself wasn't nearly as terrifying as I'd imagined it would be. I think, in all honesty, I was going in there feeling as though I was facing a viva, whereas it was much more of a friendly chat. Naturally, you have to display your skills, enthusiasm and knowledge, but in a much friendlier way than a viva (from what I've heard about vivas that is...) I had to give a 10 minute presentation about my proposed project, which I did via PowerPoint. The panel asked me some questions afterwards, about my proposal, my interests, why I wanted to do a PhD and how I felt I'd cope with the demands of the PhD programme. My supervisor was great in helping me prepare for my interview, and making feel less panicked about the whole thing.
Essentially, across all the different applications, I was working towards being accepted for around nine months. That's a lot shorter than some people and a lot longer than others. The key thing I'd recommend? Be passionate and enthusiastic. When you feel those things about your project, the rest comes a lot easier.