I was private for mine, so did not have much of a wait between meeting the clinic and starting a cycle - for my most recent cycle I went for the planning appointment and started a couple of weeks later.
There are two main protocols - long and short. I have had a cycle of each.
For both of mine they started on day 21 of the cycle before.
On the short I started noresthisterone tablets on day 21 for about 10 days then had a bleed. On day 2 I had to go for a baseline scan and then could start injections with 2 a day.
On the long I started buserelin injections on day 21 for about 2 weeks and then had a base scan. That was clear so could start injections.
Some clinics start earlier on day 1 or 2, if you do not have the bleed when they expect you could be longer etc so there are lots of variables.
Once injections started I had two injections a day, a scan after 7/8 days and then other scans as needed. For the first cycle I had 12 days of injections and on the second I had 11 but people do vary.
You then have your trigger dose and egg collection is 36 hours after. The eggs are fertilised and if you are lucky you have an embryo transfer up to 5 days after that.
Clinics seem to have different lengths for testing dates, but mine was 13 days after transfer.
For both, we started on day 21 of one cycle and the test would be the end of the next cycle, so around 6 weeks. However, each clinic is slightly different and everyone can react differently, so that timescale may not be accurate for you.