As Vatta mentions, it does really seem to vary depending on what part of the country you are in.
I also had a spreadsheet charting my cycles which is helpful as you will constantly be asked how long your cycles are and the date of your last period.
As you already have a DC, it may be something quite simple in terms of a few tests and medication for one/both of you, but I'll share my experience of IVF in case it helps a bit.
I hate to say it but my advice would be to prepare yourself for the fact you will possibly have to self fund any fertility treatment. Based on my area of the UK (The Midlands) you wouldn't qualify for NHS funded treatment as you already have a DC (there are a few factors including weight, age etc that would disqualify you from receiving funding too, and even then you only get one funded cycle)
We had been TTC (our first DC) for about 3 years with no success, though it was probably different for us than it will be for you as the reason we were not conceiving was quite clear (DH has retrograde ejaculation caused by diabetes and he had undergone a couple of initial investigative tests a couple of years before hand which hadn't amounted to any actual results/official diagnosis etc.)
We decided to start from the beginning and it was very simple, just a normal appointment with our GP - he had a quick look at our notes but didn't really ask any questions, just said I'm going to refer you to a private clinic for fertility treatment, it's clear you have been trying long enough. (This was October 2012)
We were initially referred to the fertility department of our local hospital and I had blood tests on day 2 and 21 of my cycle to check I was ovulating and also a chlamydia test. We had a couple of appointments with the head fertility nurse at the hospital to complete our application for IVF funding on the NHS where she explained exactly what we would 'get' on the NHS. Also more blood tests and screening for HIV/hepitias for both of us were done (all legally required for treatment)
We got an info pack through from the private clinic and had our 1st appointment in May this year.
Once we were under the private clinic's care I had an internal scan to check my ovaries, my DH had a couple of operations to surgically remove and freeze sperm, then they ordered and delivered medication for me.
I did about 10 days of hormone tablets, then 2 weeks of 2 different injections, (with internal scans at the clinic every other day for a week to check the injections were working) then one last trigger injection before going under sedation to have my eggs collected, fertilised with DH's sperm in a dish (a process called ICSI) and the fertilised embryo transferred back into me a few days later. (they also froze 3 other embryos for us to use another time when we want DC2 etc) NHS funding in most areas only allow 1 embryo to be transferred back to prevent multiple pregnancies.
I had to wait just over 2 weeks after that but then got to POAS and we are so lucky to have got a BFP and I am now 8 weeks pregnant.
So from the initial GP visit to getting the BFP it was about a year, though we did have a lot of delays and problems getting paperwork from the NHS to the clinic which held things up quite a lot.
We actually found the whole process quite straightforward once we had got going with the treatment.
Obviously it will all be different for each couple depending on what the actual issue is - ours was probably quite easy as it was clear what the problem was and everything with me was fine.
My DH didn't have to do anything except have his sperm removal op. (Most blokes would have to provide a sample in a pot instead of that part.)
Also, I understand you have a lot more options if you are paying privately for treatment.
Not sure how useful my experience will be but happy to answer any questions if you like!
Good luck with everything!