I am in Australia, so I expect the timeframe for referrals etc is different here. Exact procedure will depend on your circumstances. In general it will involve 2 weeks of hormone treatment to stimulate your ovaries to produce more eggs than just the usual one. These treatments are usually injections you do yourself at home, but they are easy and painless. Then on egg collection day, you go to the clinic and the eggs are retrieved via a long needle/tube that goes through the vaginal wall into your ovaries. For me, that procedure was done under light general anaesthetic, but I understand in the UK it is often done with local anaesthetic. Either way, it is pretty painless - I was back at work the following day. Your partner provides a sperm sample on the same day.
Then, like you say, sperm are injected into eggs and hopefully some will fertilise and start to grow. Your clinic will keep you informed by phone on progress over the next few days. Clinics have their own ways of deciding at what stage the embryo should be transferred into the womb, and how many to transfer. My clinic preferred to transfer 5-6 day old embryos (called blastocysts) and would only transfer one for any given cycle. UK clinics often seem to transfer 3 day old embryos and are more open to transferring two at once. Either way, the transfer is pretty straightforward - cervix opened and long tube inserted through vagina into womb. No more unpleasant than a cervical smear. Again, I was back at work next day.
Then it's just a 2 week wait to see how it goes. That is probably the hardest part! You may be given more hormones following egg collection and embryo transfer, but that depends on whether or not your clinic has decided to 'stop' your natural cycle. For me, the hormone injections done before egg collection had no obvious side effects. The hormones afterwards gave me nausea. Emotions were up and down, but hard to say if that was the effects of the hormones or just from the stress/excitement/nervousness about the whole thing.
We never got to the stage of considering 'just not doing it' because we were lucky enough to be successful first time. My age meant that we really didn't want to keep trying for natural conception and may have made adoption difficult, although that wasn't an option we really considered.