I know some of you have already BTDT or started earlier this season, but I do know I have some readers expecting their first mammal babies and maybe a little bit nervous about it.
My feeling is that there are three things you should remember in kidding.
1. 99% of the time, the animals should be able to do this fine without you.
2. Even if you have to intervene, 99% of those times, everything goes ok.
3. It gets easier if you know what to expect.
Here's a (very silly, non-technical, done by someone who likes to make a big deal of how gross it is - of course, he's a guy and never given birth himself) video that will give you a rough sense of a normal kidding (it was quads). Do note if you don't want to see animals giving birth, you shouldn't watch these videos - don't whine about it in comments later.
This is a much less silly video of a delivery of abnormal presentations:
Note that it is possible to handle those things with comparative aplomb, even though you are scared out of your wits.
If you are expecting babies you've probably read everything on the internet twice, so I won't duplicate that information, just note that kidding or lambing is a lot like hitchhiking the galaxy - Don't Panic! and have a towel handy.
The music in the first video was nauseating. Beyond that, I don't think they're going to thank us for the fish. ;)
I think one of the keys is that you limit it to kidding and lambing and not just livestock giving birth. Having raised sheep, cattle and pigs, pigs need the least help, sheep need a little more help (probably more than 1% but less than 5%) and cattle need more help.