I have had two sections - both technically emergencies, though one more urgent than the other. Both after long labours.
I need to point out now that epidurals don't work great on my - so don't take my experience as a given!!
The first - induction, drip, epidural etc - I needed a stronger dose of epidural as though numb on outside, could still feel contractions internally (wasn't believed until I was yelling through gas and air, with epidural in place for a while!)
c-section called due to failure to progress, all stopped around 8cm. They topped up my stronger dose of epidural just before starting, then double checked there had been no magic change (there hadn't) ... they put up a screen so you can't see the gory bits, but having removed my glasses it really wasn't necessary! Opened me up - and DC1 was out within 5 mins - this time varies, then wrapped her in a towel and gave her to SBXH (then DH) to hold on my chest so I could see her. Whilst I was cooing they stitched me back up - didn't do any of the weighing etc until I was in recovery so I could watch. I don't remember huge amounts of the op as had been awake for 3 days at that point! In recovery they weighed her then put her on me skin to skin so she could have her first feed. Then they dressed her in outfit I pointed out and snuggled her up with me,
Second time around - sponaneous labour... won't bore you with the details but the crux is it all stopped again at 8cm so off we went to theatre, the difference being DC2 had started to become distressed (an even longer labour than first one... not surprised he was fed up!) so they whizzed me in and did epidural. Anaesthetist was amazing, talked to me the whole time - they opened me up and had DS out before they had switched on the music! As he was being shown to me I started to feel sick, they moved him away (just in case) and shot me with some antisickness stuff in my IV.
A second epiudural close up normally takes longer as there is already scar tissue, they try to tidy it up as they go - but anyway I was starting to feel tugging - told the anaesthetist, who gave a significant look to surgeon. They continued and I need to point out here I was perfectly calm, felt completely looked after. The tugging got sharper so I told them I could definitely feel cutting now (just an ouch type point not agony) ... so the anaesthetist asked them to stop whilst he sorted the pain relief ... they couldn't as I was haemorrhaging so he had to knock me out - mask / gas stylee... apparently it was only a light knock out - he told me what he was going to do, I was calm and relaxed (strange I know!) he flipped a switch, suddenly it was harder to breath so I was forced to take a deep breath and off I went. woke up in recovery all sorted. DS was weghed in theatre this time so I had already seen it. He was dressed and snuggled up to me and all was good with the world.
I didn't write that to scare you , more to reassure that if something doesn't go to plan - it can still be perfectly positive experience. Technically the epidural wore off (wasn't the stronger dose) , technically I could have died - I didn't. My experience with DC2 was more positive actually than my first, because I put my trust in the staff - who were amazing!