I'd wondered about this, should I ever have to testify in court (to date, I haven't). Cecil Adams of The Straight Dope comes through:

When a witness refuses to swear to God, the court accepts an "affirmation" instead. In a jury trial, the smart lawyer will arrange for this ahead of time in the judge's chambers, so the witness won't look unduly obstreperous or morally deficient in open court. The judge may then instruct the jury that the funny oath they are about to hear should be considered legally valid.

In U.S. District Court (to take the most widespread example), the standard oath is amended to: "You do affirm that all the testimony you are about to give in the case now before the court will be the truth, the whole truth, and nothing but the truth; this you do affirm under the pains and penalties of perjury?" After the witness replies, "You got it, Jack," or whatever godless heathens say in such situations, everyone sits back and pretends that the "pains and penalties of perjury" are every bit as intimidating as the wrath of a vengeful Almighty. It's not an ideal situation, if you want my opinion, but I suppose it's the best the judges can do under the circumstances.

If I ever do have to swear in court, I'm using "You got it, Jack".