Keep in mind that every thing I write about will not hold true in all cases, but for the majority of them it will. First thing to look for is what we call "springing." If you get around behind the cow and look at her vulva you will be able to tell right away what I am talking about, especially if she is walking. Most cows vulva's are pinched in and tight without any loose skin, but come calving time you will notice that there is an awful lot of sag. There can be several folds of skin underneath the vulva, and the cow literally will bounce all over the place when she walks. When you start seeing springing keep them up by the barn because the calf is on the way.
The second thing to look for, as has already been mentioned, is an enlarged bag. I have noticed that this isn't as reliable as I would like it to be. Some cows don't develop much of a bag until after the calf is born. If you see the cow is springing and has a tight bag, they should be getting pretty close. If you happen to see a real thick chunk of mucus on their tail they will probably calve within the next two or three days.
All of these are pretty good signs that the cow is getting close, however I have seen cows calve that didn't even have any signs showing, so they aren't 100% accurate. The surest sign of all is strange behavior, but that is probably also the most difficult for a rookie to recognize. The behavior will usually consist of a cow switching her tail back and forth and occasionally kicking at her belly. They might also be pulling their ears back. Generally speaking, they will be displaying signs that they don't feel quite right. Quite often the cow will leave the herd and try to find a secluded spot. When a cow starts exhibiting these signs you know the calf is coming within the next few hours.