- you attend an information evening
- you register interest
- social worker does a home visit
- You start stage 1, this is where social worker does a number of visits to assess whether you meet criteria to move into stage 2 (health, finances, what support you can provide a child, whether you have the work life balance to support it,CRB checks, whether your understanding of adoption is realistic, what your support network is etc.) You normally do between 1 and 2 training days as part of this. You complete a written workbook about all mentioned.
- If pass stage 1, go to stage 2. Training days, roughly 3 days. Further assessment by social worker through a number of home visits (we did about 6-8 2hr sessions), looking much deeper into everything you put in workbook, so social worker can put together a report. Your friends and family will have to write references and be interviewed.
- Go to approval panel (panel of up to 10 people in a room, a bit like an informal interview with yourselves and your social worker being questioned) - if they agree then you're approved to adopt!!
That should all take about 6 months but they can stop the clock, if say you need to get more experience with children, to give up smoking etc..
7.Then comes matching, where social workers try to match children waiting to potential adopters. This involves different reports, meetings, matrixes, approvals, comparisons and lots of phone calls, a bit hard to sum up really. Adopters can be asked to attend matching events where profiles of children waiting are displayed, or even where you get to meet children waiting (note, other than this you don't tend to meet the children who you will adopt before it's all decided). If you are an agreed match with a child, then more report writing for social workers, you get to have meetings with child's social workers and their foster carer, read lots of reports and see DVDs/photos.
- Go to matching panel. Exactly same set up as approval panel but this time all questions relate to the specific match of you and the child and what you will do to meet their specific needs. If they approve match...well...you cry a little, get very happy and then panic a bit!
Matching can take any length of time, from weeks to years.
Note there are additional training days to do, we did another 3 between approval panel and matching panel.
9.Once matching panel agrees on match, adopters make a DVD or book about themselves and where they live, although most will have done this already and taken it to matching panel, but this is now shared with child/children.
10.Intros begin where you spend time at foster carers with the child/ren and then at yours (this in all takes up to 2 weeks), then you have placement day - moving in day.
11.Then social workers visit every 3 weeks (ish) and you have reviews every couple of months with 3-4 social workers descending on your house. In this time you may also meet birth family. SW's complete yet more reports on everything, all eventually leading up to a court date, where birth parents may or may not contest. If it all goes through you then get a court order known as an adoption order, at which point all legal rights as parents are passed to you and the surname of the child changes. You have what's known as a celebration hearing at court, once this is granted. Following this the social workers stop descending and you're then just committed (with regards social services) to whatever contact arrangements you signed, commonly 'letterbox' where you write to birth family once or twice a year until your child is 18.
That's the basics, others may be able to give more details on certain bits and there may be slight variations on training etc. per adoption agency. I've experienced it as an adopter but I'm no expert 
I am however a bit of an insomniac at the moment so thought I'd give an answer