in simple terms you're right. here's a slightly longer version.
there are two types of IVF, long course and short course. depending on why you need IVF will depend on which course you start on and what dose of drugs you're on.
the long course you will start something called a down reg before you start stimulation. this will switch off your natural hormones so that the hospital/clinic are in complete control of your cycle. short course you go straight to stimulation missing the down reg, this is normally the course picked for women who they worry will over stimulate and could end up with OHSS. even though it sounds great being over stimulated and having tons of eggs, it is actually very unhealthy and can be quite dangerous.
once you start your stims you will be scanned every few days. this will check how many follicles you have and the size of them. most clinics look for follicles of 16mm or bigger before they will try for collection but they can works with smaller, so its not always a huge factor. so the stims can last anything from 7 days to two weeks, depending upon how quickly your body responds to the stims (personally my first round look 15 days, second was 9 as I was on short course)
note - each stims is different for each woman, I had injections that I had to administer at home. for the first 5 days I had one lot of drugs and then on day 6 I started a second drug, so I ended up having one injection in the morning and one in the evening. but each woman is different and different courses use different drugs, so this isn't guaranteed.
on egg collection day you will be put under a general anesthetic where via ultra sound, they will guide a needle to your ovaries via your vagina (they will pierce your vaginal wall in order to get to your ovaries - its not painful but you can be a bit swollen for a few days afterwards). they will puncture your follicles and drain them of the fluid inside - which can contain eggs (its not a guarantee that a follicle will contain an egg, so it could be empty) the hospital/clinic will tell you on the day how many eggs they were able to get. but they will not be able to tell you quality at this stage - quality is only discussed at transfer stage.
once all your follicles have been emptied, an embryologist will take the liquid straight to the lab and start going through it to look for your eggs. after this it depends upon whether you're having standard IVF or ICSI (ICSI is normally used when the sperm are not top quality or they believe the sperm may have a difficult time penetrating the egg). with standard IVF your eggs will be mixed with your partners sperm in a dish and left on their own to fertilize. ICSI your partners sperm will be cleaned and a single sperm will be chosen and injected straight into the egg.
after this your clinic will be in touch within 24 hours to let you know how many from your original number have fertilized. its not a guarantee that if you get 7 eggs, all will fertilize, so the more eggs you get, the better your chances are of one of them fertilizing.
after this, your hospital/clinic will try to go for a day 5 transfer once your embryo has become a blastocyst. hospitals can put your embryos back in sooner if they feel that it would do better inside your body (my first round went back in on day 2 - I only had 3 eggs and only 1 fertilized. on my second attempt I had 15 eggs, 12 fertilized but only 5 were of decent quality to work with. I had 1 day 5 embryo transferred and 4 put into the freezer)
after that, once your embryo is back in, its the dreaded two week wait where you will slowly lose your mind haha
with regards to how they work out a cycle, my hospital classed 1 cycle as everything up to 1 fresh transfer (so a day 5 embryo that had not been frozen) any frozen embryos that we want to use we will have to pay a fee to use. each hospital and clinic are different, so that will depend on where you go.
with regards as to why IVF doesn't work.... that's a hard question. I have no idea why my first round failed and neither did my consultant. I know women who had top quality embryos put in and had such a healthy lifestyle and did everything right and for what ever reason, it just didn't work. but I know of women the other way round who had slightly worse quality embryos and now have bouncing babies. there is only ever a 40% chance that a embryo will take regardless of quality (according to my consultant)
I hope this answers your questions. IVF seems daunting but I always feel that the more you know, the better prepared you are for whats about to happen. my first time I felt worried because I didn't understand the lingo and process, second time I was a lot more relaxed. so don't be scared to visit a clinic and discuss your options, you'll feel better for knowing what's happening and what you can do.