Just had my third one today! You'll probably get different answers from people, but here's what my doctors have told me.
They will do an internal exam with one or two gloved (and lubed) fingers to see how your cervix feels, if it's soft or open at all. Then they press into the opening of the cervix and literally sweep the finger around the opening, separating the membranes from the cervix. It's a very quick couple minute thing they do in their office. Some places won't do it before 40 weeks, others will start after 37 weeks.
Effective? I've heard 1 in 8 it works for. I've also heard that it does an excellent job at stimulating hormones so that you don't go too far overdue.
Risks? Seemingly extremely low. It's a natural process that doesn't involve much actual "work" there. If baby isn't low enough it can possibly cause a cord prolapse, but that's in extreme situations. It will cause spotting or bleeding. It does not and should not break your waters. I've heard there is a chance that it can break your waters, but that's only if it's not done properly and is an extreme rarity.
For me, I had one at 38 weeks, 39 weeks and finally today at 40 weeks + 5 days. Each were fairly painful, pinching kind of feeling, not fun! It's so quick though and I figure labour will be way worse, so I went for it. I had spotting with each of them, cramping and aching for a few days after. With the other two everything went back to normal within a couple of days. Today though, I hope this kick starts something!!!!