First of all you need to find an architect. Make sure you are specific about what you want and what you want it to look like. Otherwise it could become very expensive.
Once the design is what you want, go and speak to your local planning department before you submit a request for planning permission. They can give you hints and tips about what they are looking for and what regulations they have to adhere to. If you do this first it should save you time and money.
Once you think your design will adhere to what the council will approve, submit your planning permission application. Have a look on your local councils' website as the planning department will probably have posted useful information and application forms.
Whilst you are waiting for an answer from the planning department (usually a month) start getting quotes from builders (ask friends and neighbours if they recommend anyone.) It is also worth hiring a builder who will deal with building regs for you - they have more experience than you do.
Once planning permission has been granted and you have chosen your builder, you can than get started.
I would say that best case scenario, if you started getting things moving today you may be able to start building in 3 months.
But there are so many variables. The architect may have to do various versions until he comes up with something you like. The builder you choose may not be able to fit you in until x months time. You may not get planning permission first time and you may want to appeal. I think you get the drift!
I have no idea of costs, again it depends what you want to do. What windows, doors, electrics, plumbing you require.
I bet loads of people have answered before me now (I had a Tesco's delivery mid flow!)