You basically can't.
There are six banks leading the IPO: CS, Deutsche, Goldies, JPM, Morg Stan, and Citi. This is an incredibly hot IPO - they're closing the books early and increasing the price range, which they wouldn't be able to do if there wasn't huge demand - and that means the banks can give the IPO shares out to their favourite clients.
And that means you have to be a client of one of those six banks, and a VERY lucrative client at that. If you're a private bank client, you might get a tiny slice if your relationship banker likes you and has enough clout to lobby his higher-ups for a slice to give out to his clients. If you're a regular wealth-management client (or, worse, a regular client) you're not going to get anything.
For what it's worth, I have a (small) account with JPM, and I've had MS pitch to me pretty hard before, dangling IPO shares in front of me if I bring my account over. I haven't heard a peep out of either of them about Alibaba, which makes me think that small investors like me aren't going to get squat. It's all going to the big guys - the Fidelities and Blackrocks.
Now, there is a semi-sort-of-back-door way of doing it, and I'm going to mention it here because if I don't some smartass will pipe up and say "hey you forgot this!" and make it sound like a good idea. Yahoo and Softbank both own big chunks of Alibaba - they're selling some in the IPO, but they'll still own a bit. So, technically, if you own Yahoo, about 10-20% of what you own is actually the value of Yahoo's stake in Alibaba.
That said, the other 80-90% is miscellaneous Yahoo rubbish. So it's entirely possible that even if Alibaba screams higher on IPO day, that Yahoo or Softbank might close
lower, just because the companies are so much more than just their Alibaba stakes.
So don't get any ideas about buying Yahoo or Softbank as a second-order punt on the Alibaba IPO. This is a classic muppet trade, and the odds of it making you money are basically no better than a coin flip.