The following is meant as a guide with a few extras on applying to Universities in the USA and France. I started from knowing nothing about the process and could have done with something like this about two years ago. Any comments or criticisms are welcome.
1. It takes time
a) My brother says that applying to jobs is a full time job, I would say that applying to Universities is just as consuming. Obviously the more Universities you apply to, the longer it all takes, but the point to get across (that I didn't fully understand) is that all the form filling, reference gathering, proposal and statement writing... it's hard work.
b) Because the whole process takes so long you need to start as early as possible and you need to be patient. The moment you're thinking of applying you need to start working, looking for possible Universities, contacting lecturers and asking administrative staff questions. These people aren't going to get back to you straight away with the answer you were looking for so you need to be patient.
c) Deadlines are often a little flexible but it's not worth the hassle of testing them.
2. You need a proposal
a)This is usually a two to three page document outlining the area of interest, the approach you're going to take and the reasons that other people should be interested. It will reference other work in this area of research, be clear and concise and get people's attention. If you're applying to lots of different Universities it's very likely that you will have to tailor this document to the department to which you're applying. If you're reading around the topic while you're working on the proposal it's likely that the last draft you write will be better than the first. You might want to think about this with regards to the order in which you apply to the different Universities, especially as they'll all have different deadlines.
b) People often say that it's hard to describe the "focused" yet "broad" lens that a research proposal/topic needs to capture. I think that you know it when you see it so my advice is to read as many other people's proposals as possible. It's true what people say, the best ones really can be very narrowly focused and at the same time speak to much broader and cross-disciplinary issues. I think that this is often conveyed in your tone - you've skillfully picked up on a new way to take the literature and you've got a huge amount to say about it because it relates to lots of other things.
3. Lecturers are interested
a) I thought that I would only get a few polite "thanks but no thanks" messages when I sent my proposal to different lecturers but I've since realised that answering the "I'm interested in your work/studying at your University" emails are lecturers' bread and butter (a standard, wholesome process). If the lecturer has even the smallest interest they will write back with helpful tips. It goes without saying that these email exchanges are going to show you which University is going to be more supportive of your work.
b) The same goes for referees. I was in the position where I had lost touch with the people that eventually became my referees for my masters degree and then graduate degree applications but they were extremely pleased to hear that I was back into anthropology and more than happy to be referees.
c) Talk to everyone and anyone in the department to which you're applying. Students and lecturers will be pleased to hear from you. The funding and admission meetings will include people from the department that you don't know and maybe even a few students. The more people that know your work on the panel the better.
a) Don't be shy. They want to hear from you and know what you are up to. Send them any work you've done and tell them about your projects and plans. It all goes into making a good reference. The more they know about you the better. If they haven't seen your work they can write a "qualified reference" that says "this student is good as far as they go but I haven't really seen enough of their work to tell you if you should have them". Remember you aren't supposed to see your references.
US Universities -
a) Sometimes you're applying to work with one or two lecturers sometimes you're applying to the department. Find out so that you can tailor your application.
b) Use titles. In the UK you can drop titles pretty quickly. In the US, if you know someone is a Professor call them "Professor" ... otherwise use "Dr".
c) It costs quite a bit of money to apply to US Universities so you need to do lots of research before applying.
d) When you apply to US Universities you are often applying to be a research assistant or a teaching assistant.
French Universities -
a) Basically there are loads of state run Universities that are more or less free but much less prestigious than the private Universities. If you can find the person you want to work with at a state University you're in luck. Otherwise you will have to pay to go to one of the private Universities. I don't know about securing funding for these (anyone?).
b) You'll have to write your thesis in french so you'll have to be near perfect. BUT what often happens is foreign students write in their version of french (which might be slightly off in terms of tone or register) and then their friends edit or even refine it.
c) You're encouraged to be involved in the full PhD experience with your fellow students but because you don't have to go into the Universities too often you could get away with living in another European country. Not that you'd want to... France is a great place to be poor.