It was the same for me, I was a bit in the dark about what was happening. Also costs kept coming out of nowhere which was hard since I was privately funded.
From what I remember: I went for initial consultation in August and was talked through some of the key steps. Then I had an internal scan of my uterus and ovaries. Then a consultation with the doctor. Then some bloods and a HyCoSy which happens in theatre (probably the worst bit of the whole procedure, it's so they can check your tubes are clear). Then because I was using a donor, I had consultations with a counsellor (to make I understood the implications) and then with the donor team to talk about the process. I decided I wanted to use a donor through the clinic rather than arrange my own (there were a limited number of banks they accepted sperm from), so I went on the waiting list. All of this process took from about August-Novemberish.
I went on the donor waiting list at the end of October or early November (can't remember) and was told I had a match early January. I made a decision pretty quickly, and after that if the donor has any matches for carrier status (and they usually do, most people do) you have to discuss with a genetic counsellor and they tell you what it means and what % the risk is. You can have your own genetic profiling done privately at this point if you want, but because the mutation he had was so rare I didn't think there was much point plus it isn't a test they typically do, so I decided to progress straight to treatment.
Once they receive the donor sperm at the clinic, the consultant will put together a "protocol". For me, because I'm fairly young & no known issues, I was asked to take minimal medication for a few days the day after my period to kick-start ovulation. It's a private prescription but you can get it from the Tesco pharmacy and it wasn't as expensive as I thought it would be. Then on about Day 7 of my period, I had to go to the clinic first thing every second morning to do bloods and an internal scan, to see if my follicles were growing & if I was ovulating.
I think I did 3 scans in total and they were happy with the size of my follicles but ovulation hadn't started yet so they didn't want to risk multiple being released (they try to avoid multiple pregnancies) so I had to give myself an injection to start ovulation, then the next day they did the IUI. The IUI bit was actually super quick, then they make you lie there for 20 mins and then you can go home and do a pregnancy test if you miss your period! I tested positive early March (my first cycle).
TLDR; it was approx 6 months from first contact to the actual IUI happening, and 1/3ish of that was the sperm donor waiting list. And then a painful 2 weeks waiting to find out if it worked or not...