Most women on their own with kids are looking for two things: sex, and someone to share the joys and sorrows of life with. If you are mainly interested in provided the first one of these, the kids don't even have to figure in your relationship at all. So, if you're interested in a woman and suddenly she tells you she has kids, just say 'Fine'.
The only thing that is different than dating a childless woman is that you probably don't want to go back to her place so you better make sure your place is clean and comfortable. Oh, and she won't want to stay the night without at least a week's notice - but that can be a good thing. A lot of guys don't particularly want their dates still there in the morning anyways.
A divorced or single parent can be a great person to date so long as you accept that when it comes to the important stuff, the kids are going to come first. Most women know enough not to cancel a date every time little Joe has a cold, but if the sitter doesn't show there's probably not much she can do except stay home. This can be very annoying but you should remember that it is not your date's fault and she is probably just as annoyed as you are.
Look for ways to work around the situation. Most times this would mean rescheduling the date. If she really wants to see you she may suggest that you go over to her place. Dates at her place, however, are best avoided until you know her well, unless the kids are really small and likely to be safely asleep the whole time.
When it comes to a relationship, or having several dates, there are a few things that start to be more important. For example, at what point do you meet the kids? Unless the kids are very young, this is best avoided unless you are serious about the relationship. The kids will almost certainly see you as a potential stepfather and there is no point in creating the issues that they will have over that unless you see yourself that way too.
So if you find that a woman you are interested in dating has kids living with her, there is no need to let that be a problem. You can date her and get to know her just as you would anyone else. Dating women with kids is not so different from dating childless women.