Q) Could you guide me a little about the general application process?
A) Well my first answer would be sit online as much as you can and start looking at universities you would like to go to, what programs they have and what are their deadline. Deadlines are important to keep in your head.
Generally speaking, some school have two rounds of admissions: an early and a regular. The early usually makes you commit to the school if you do get admission. The regular is just a normal application, no strings attached-that's what most people do and that is probably what you have time for now. Most deadlines for US universities regular admissions will be late Dec, and may be early Jan. UK oxford and Cambridge (you can only apply to one) are earlier, rest are I think through a joint form that can be filled online called UCAS, which will i think have deadline say early Feb or something. Look at the unis you want to apply to, see the deadlines and according to that.
In the US you have something called a "common application" and in the UK you have "UCAS". These are like one application accepted by a bunch of universities. Some universities require separate applications.
Usually what they will ask for is your school transcript, one or two recommendations from a teacher or someone, a personal statement (an essay, depends on the school's topic), and O levels grades (and A1 if you apply in A2 i guess.
If you apply to the US you will need to give SATs, which you should register for soon if you plan to do that. If you're planning to apply this dec or something than give exams before that; sometimes they accept Jan ones as well. Almost all schools require SAT1 (reading, writing, math) and some require upto usually 3 SAT2s (for a particular subject) which may depend on what program you apply for. You will need to study for those a little bit so plan for that.
That's kind of it. I know it seems like a lot but you have time. Ask around for help. Just keep things in mind.