Birthing

Just remember that this about Sheep birthing. The sheep will know what to do and you're only there if there is a problem and to start the lamb off in the right direction "if" they need help.
Assuming your sheep graze freely, you might notice the pregnant ewe start to move beyond the normal range of the flock when the time is near. Either she's not feeling well (which is possible) or she's sensing labor begining and is looking for a secure spot where she's not so vulnerable.
I've always felt it was a nice surprise when the ewe have felt secure enough to seek comfort near or in the barn where they know I frequent in the mroning; I guess they feel I'm OK after all. But you may also find that the'll seek our the tall grass or somewhere in a corner fence pocket nearby the feeding area. In my case, the location was almost always near the barn and I've missed all of the birthings; the closest being once when I saw the mother get up just after birthing. Even so, my sheep seem to like giving birth very soon after midnight, perhaps using the cover of darkness to help hide them when they are vulnerable.
Being that there are many people out there today on the internet who are much more knowledgeable in this area I thought it best for you to look at a couple specifics that I found helpful:
Step By Step Pictures of the Birth
Correcting a Lamb's Position During Birth - Video Presentation
Managing of ewes and suckling lambs from birth
The Placenta

The placenta will sometimes stay in the ewe for several hours after birth. If you've never seen one you might be tempted to think that the green gelatinous mucus you found was it; Nope. That's a simply a thin covering around the lamb, a water sack of sorts which the mother normally licks clean.
What you're looking for looks like this picture
The placenta "must" come out on its own no later than 6-8 hours after birth or else the ewe will risk developing an internal vaginal infection. One way to help along its expultion is to simply RUN the ewe by chasing her around a bit. Don't do this unless you're sure there is
a problem.
Chasing the mother away from the baby has given her precious little time with it. Without bonding time, and perhaps feeding the lamb, the ewe may forget and later reject the lamb.
Nevertheless, the jostling caused by running will often help shake the placenta loose, and if it doesn't, you should call a vet. as soon as your overly suspicious. I know running the ewe is not a nice thing to do, but it's cheaper than a vet call.
Once expelled, the placenta weighs about 2 lbs and is about a 1 quart volume (Picture above - they all look like this - one big jellyfish about 10 - 12 inches in diameter on flat ground).
WARNING. . . .
Please, listen to experience:
"BURY THE PLACENTA
As Soon An Possible
& BURY IT DEEP"
Dogs of any type such as strays, coyotes, fox, or wolf will smell the placenta and come running to look for an easy meal; they won't stop at the placenta but go right for your new lamb/s or mothers who are standing at their side.
Not once have I had lambs and didn't see dogs the next day around my fence line -- BE AWARE, check your fences ahead of time, keep a rifle, pellet gun, pistol, paintball gun, or air horn handy to help drive them aay or kill them. Burying the placenta eliminates and reduces the odor much more quickly; lowering your risk of preditor exposure. Bury it a couple feet down -- the post hole digger will make the job much quicker and easier.
The weight loss from the placenta and the lamb (~6 lbs for a single) means that the ewe has dropped nearly 10 lbs that morning (~15% of her pregnant weight) .
Within the next 48 hours the ewe will continue to loose some water weight urinating until she once again reaches her normal weight. The stretching of the stomach will leave her looking a thin just forward
of the hips for a week or so.
This ewe just had twins (5 & 4 lbs + the placenta weight)
Note the heavy 'dent' just forward her hips
Possible problems with Twins and Triplets

We all strive to find and keep ewes that give birth to multiple lambs and are able to sustain them until weaning. But ewes that havn't yet had twins may have their special challenges at the start.
Lambs take about 24 hours to learn who their mother is and know her voice, obey, and follow. If the mother isn't recognizing the lamb as hers, then you may be stuck with something called a "Bummer"; and boy is it ever a bummer -- hence the name.
There are several theories about why ewes might reject their young, even experienced mothers. My observation is that ewes with multiple births will have their first lamb, get up and walk a distance, all the while still having contractions, lie down someplace different and have the second. Perhaps they may get up once again and move on and have the third.
The mother normally will smell and lick the lamb clean, bonding with the lamb and recognizing that it's hers. But walking awy and giving birth to the others, that may not happen.
This ewe birthed lambs on opposite ends of the corral, forgetting she
had two. The first was brought back and placed near the ewe, face
force buried in the lamb for about 30 minutes while the other lamb
hovered about . . . she accepted it back.
"Ideally", the ewe having multiple lambs should be confined (If possible) in a well lit stall while giving birth so that both lambs are very close to the ewe and can't stray. Please notice I said "Ideally". There is a certain amount of credit we need to give God for instilling the motherly instinct in these sheep. In the pasture/wild, sheep can manage twins and triplets just fine, but, "Ideally" means that you are trying not to loose a single lamb -- which happens more often in the wild.
If the weather is cold, if the time and place are dark, if the area is overcrowded and/or noisy, the weather is rough and rainy, and if the mother is just laboring too hard, the ewe may simply forget that she dropped the first lamb and never go back to retrieve it - especially if the lamb is tired and passes out without making a noise. This happen twice for me, once the lamb was rejected, the second time I forced the mother to smell and lick the lamb for 30 minutes -- and she accepted it back being that it was so soon after birth. And this was from a ewe that was a great mother to her first birthed lamb.