Okay, so first I should point out that I am stating these factly opinions (oxymoron? I think not) as a religious Jew.
Obviously it is impossible to prove that G-d created the world-- you can have faith He did, but you cannot bring evidence. Therefore, the only shot you have at winning this debate is by proving that creationism and evolutionism do not contradict (as they do not).
Now, take a look at Genesis. It says G-d created the world in seven days, clearly violating evolutionism as the world was created over hundreds of thousands of years, and traditional Jews will tell you that the year is 5770 since Creation. You must realize that when the Bible says seven days, this should not be taken literally as days, but as time periods. (There is a proof that the Bible sometimes uses "days" as "time periods" somewhere, but I forgot where so you'll just have to manage without it.) Now, take a look at the seven days of Creation: Light, sky, heaven and earth, sun and moon, fish and birds, reptiles and animals and humans. If you look at the order, it really doesn't contradict the chronology of evolution! Three days are spent creating the earth and the universe itself, then the fish (keep in mind that not everything should be taken literally, this can mean anything that lives in the ocean), birds, reptiles, mammals, then humans. Coincidently (not really), this is the same time order of evolution, from a biology point of view.
I thought I'd also mention that some Jewish commentators (Maimonades maybe? Can't remember exactly) say that all G-d did was create the first spark of energy, and that eventually snowballed into all of the world and everything you see before you, which is a pretty neat idea.
It should also be noted that the Bible never mentions dinosaurs, so if your opponent brings this up, there are several places in Talmud and some commentators say (Vilna Gaon I think?) that G-d created several worlds before ours and destroyed each of them-- dinosaurs are remains of previous worlds, so they really are tens of thousands of years old. And the earth really is millions (billions?) of years old because it was used by previous earths.
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I know I am probably opening myself up to having to sit here all night debating with people, but as an educated Jew I believe (and I'm sure most other Modern Orthodox Jews believe this-- and not trying to be pompous or something, but Modern Orthodox is really the best place to be-- you are religious and follow all the commandments, yet you aren't so overly religious that you aren't good to people, and you follow the Torah logically and precisely. Chassidim would just dodge the question and tell you to follow the Torah wholeheartedly and Reform, Conservatives, and Reconstructionists etc. are not religiously educated and aware enough to answer fully) that science really doesn't contradict my religion in any way, in fact they go hand in hand. Many Jews from thousands of years ago were far more advanced in science than Gentiles. In the Talmud, there is an accurate number to the number of stars there are in the universe!! So really, science and Judaism don't contradict, and if you don't believe me try to stump your local, Modern Orthodox rabbi.
