We are currently in the middle of goat kidding season and I wanted to give a few tips on that subject. Most often the doe doesn't need any help at all with delivering her babies but sometimes things go wrong and you need to give assistance, especially when there are multiple babies being born in one belly-load.
First of all, you need to know when she is in labor. If you watched them breed in the fall then you probably have a good idea of when the due date is. There are plenty of pregnancy charts out there to plug in the breeding date and get the estimated kidding date. If you let them pasture breed, then you will have to use your powers of observation, which I've found vary in efficacy from person to person. Some of the signs of impending birth are: loose ligaments, which basically means that when you squeeze or touch the goat around her tail area it feels very mushy and loose, with no muscle tone or anything. This is all the body preparing to open up for the babies to be born. Another sign is of course the udder will fill with milk. Each goat is different in that aspect. Some goats start to fill up their udder several weeks in advance but others, especially young first time fresheners only get their milk the day of or the day before kidding. Another sign is mucous. Most does when they are getting ready to kid and start having beginnings of labor have strings of mucous coming out that end. One doe of mine on her first batch of babies had mucous for about a week, but most of them just have it the day of or the day before kidding. Those are the most obvious signs of getting ready to kid.
Once she is starting labor there are other signs which include: yawning, pawing, nesting, getting up and down, being very affectionate toward you, not wanting the other goats near, etc. Then when she actually starts pushing you will be able to see the contractions. First out should be a "bubble" of membrane. Inside the bubble should be two front feet followed by a little nose. If you can see this then all is well and just let mom push the baby out. If you don't see that then there might be some trouble about to happen and you should be prepared to assist if needed. If you are not comfortable with putting your hand up into the goat to help untangle baby legs then you might need to have a reliable emergency vet phone number on hand or a good goat friend mentor who has experience with difficult births.
Some of the situations I've dealt with as far as difficult births include: breech birth where the back legs came out first. That is the next easiest birth to deal with except you might have to pull and make sure to get the nose and head out pretty quickly once the baby is coming out, otherwise the umbilical cord will break upon exiting the birth canal and if the head is still inside there is the possibility of the baby drowning.
Another situation that I've had has been tail coming out first. I've had that happen twice and in both cases I have been unable to get the baby turned around or at least get the legs coming first so with those, you just pray that nothing rips and pull gently with a downward pull, holding the baby's pelvis. Those are pretty hard to get out and pretty scary, but both times that I've had that happen the babies lived and the mommas were fine.
Another is in multiple babies, two different sets of legs try to come out at the same time. In that case you must put your hand in and sort out the legs and heads and get only one to come out first!
Another is when the legs come but the head is twisted back or tucked down. Again if you see feet but no nose you must go inside the goat again before too much of the feet are out, reach around in there until you figure out where the head is and get that head pointed in the right direction. One birth I had the head was tucked down in between the baby's front legs. I got it pulled up and started pulling but the baby tucked back down again so back in I had to reach and pull the head up a second time. The second time I kept my hand in the doe while holding the baby's chin up and pulling the front legs at the same time. It was a hairy moment (or should I say slippery moment?) but the baby was born alive and healthy.
The worse birth I've had to sort out was one of my older does. She started labor, the bubble came out, I waited, nothing happened. I didn't reach my hand right in and didn't see any feet, but wasn't quite sure what to do, nor was I comfortable putting my hand in right away. After a while and still nothing had happened I realized something was going wrong. So I scrubbed up and reached in and much to my dismay, didn't find any legs at all! I felt what seemed like spinal cord and it was laying crossways across the pelvis in a way that never ever would have been born. I felt along both ends until I found the head end and tried to get the head pointing in the exit direction but it wouldn't move. I finally got the tail side moving toward the exit and this baby ended up being born tail first. I thought it had already died so I wasn't being particularly careful as I pulled but when it came out and gasped for breath I cried. It was definitely the most difficult and scary birth I've had to help with. Sadly that little baby ended up dying after all, I'm sure due to complications from that birth but she lived for almost a week.
Hopefully these stories and hints will help you with any birth questions or problems you might have as kidding season goes along.