Labor doesn’t always start with the water breaking, and if an epidural is involved, the timing of its placement is pretty variable.
What is consistent is the onset of contractions - these start out of variable length and timing, and may or may not hurt particularly. (Mine just felt like pressure until my water broke, well into the process.) They get closer and closer together and more regular - that’s a good sign that things are getting serious (the sort-of-random ones can go on for days without doing much).
The “point” of the contractions is to open up the cervix. Ideally, it will have gotten shorter and softer on its own (“effaced”) before the contractions really get going. It starts out closed, and dilates to about 10 cm to get the baby’s head through. The amount of dilation when the contractions really get going is also quite variable - I had a coworker who walked around for a month at 7 cm, while others start labor while things were still pretty much closed up. The “bag of waters” is basically a membrane sac enclosing the baby. It can break while things have barely started, or not until the baby is crowning, or anywhere in between.
I think most hospitals nowadays want you to be at least 4-5 cm before they will agree that labor is really starting and admit you. (If your water breaks, they also let you in, because there is an increased risk of infection if you don’t have a baby within 24 hours of your water breaking.) Similarly, most places like you to be at least that dilated before they place an epidural, because it can slow down labor. The exact rules vary at different hospitals, though.
Once the cervix is dilated to 10 cm, they let/encourage you to push. The epidural may be turned down for this, or not. A good epidural is supposed to block pain without removing your voluntary control over the muscles, so you can still push when you have one - you just can’t really feel what you’re doing. (In practice, it’s not usually that good. I had a C-section after 4 hours of pushing. They just cranked up the epidural and cut me open. Once I was stitched up and they were ready to lift me off the table, they asked if I could wiggle my toes. “Sure!” I said, and did so. So then they asked if I could move my legs, so I picked both legs off the table and held them in the air. The nurses almost fainted, and started screaming at me to put them down before I hurt myself. I guess most people can’t do that.)
In terms of the actual vaginal birth, I can’t give you a personal account because I had a C-section. But tearing is certainly not universal, and many believe that it can be reduced or eliminated by stretching beforehand and by not trying to hurry the birth. Episiotomies (where the doctor cuts into the perineum to increase the size of the opening) used to be practically universal, but are less common today. More recent studies show that they often made things worse (just tear on the dotted line!), and that a tear heals faster and better than a cut.
If there are no special concerns, there’s no reason for the baby to be taken away, and hospitals usually don’t nowadays. The first hour is the best time to establish breastfeeding. My own baby was five weeks early, so she was taken to NICU for about four hours after I had had a brief look at her.
I healed quite quickly from the C-section - I was walking around with pain in a few hours, and with minimal pain in a week or so. You’re not allowed to lift anything heavier than the baby for 6 weeks after a C-section, although I understand that most mothers of more than one child end up breaking that rule and picking up the older child at some point. I did end up carrying both my daughter and her car seat after a couple of weeks - it was too difficult logistically not to.
I had less lochia (bleeding) than I think is typical for a vaginal birth - I think they cleaned things up a bit while they were getting the baby out. I think it lasted about ten days for me. But it can go on for 8 weeks or more in some cases. I think that 4-6 weeks is pretty typical. You basically get all the periods you got to skip during the pregnancy, one after the other. 