This is something i wrote a while back as a comment on someone's blog. It's regarding opening a bank account, but you need a cdi to open an account so it's pretty much a description of what you have to do to get the cdi:
"Opening a bank account without a DNI is a pretty easy process but a bit of a hassle. You go to the police Comisaria that corresponds to your hotel or wherever you're living. Each barrio has one. Ask anyone in your building or in the shops nearby which comisaria corresponds to your barrio. It may well not be the one closest to where you're staying by the way. You then pay a small fee (around 15pesos i think last time i organised this for someone) and ask for a "constancia de domicilio". The next day, a policeman will call round, confirm you're living there (in a hotel, apaprtment, wherever you are. And don't worry, they're not there to check your immigration status!) and will leave you with a signed and stamped form stating that that is your legal domicile in Argentina. I should point out that AFIP may well accept an apartment rental contract in place of the constancia but many foreigners don't have one. Short term rental leases may or may not be permissible. To save having to queue up at AFIP only to be told your documents aren't in order i'd get the constancia. I should also point out that you don't have to be physically present when the police come around. Your flatmate, hotel owner or concierge can confirm to the policeman that you're living there.
OK, so you have your constancia. Go to the AFIP office that corresponds to your domicile (again it may not be the one closest to where you are), take at least 3 photocopies of the constancia and your passport (photo page and the page of your last entry stamp into argentina) and a good book to read as you'll most likely have to wait for at least an hour. Ask for a CDI number. If they ask you why you need one just say it's for 'escritura'.
With your CDI number you can, in theory, open a bank account. The problem is that my bank, Banco Frances, won't accept a police 'constancia' anymore as proof of domicile (they did when i first arrived a couple of years ago). You need a rental contract. If you really, really need to open an account then get a short term rental for a week or so and take the contract along to the bank. You should now be able to open an account. "
What i've been finding recently is that some Comisarias are now saying they won't give you a constancia if you've been living in a place for less than 30 days. if that's the case then lie or get the doorman or a friend to lie when the policeman comes round to check you're there.