Buying a TIM Chip from TIM (SIM Card) is about as difficult as buying a SIM from Oi (that is, they'll probably ask for a CPF number). See Oi guide above for details.

TIM Chips are cheaper than Oi's at R$25 and they come with R$10 in credits. That'll be good for a few minutes' talk time - actual conversation time will depend on the State where you are.

TIM offers nationwide coverage even if it's still a bit patchy at the moment. Signal strength and quality not up to Oi's standards, but then again Oi doesn't have the whole country to cover (8.5 million sq. Km of it).

They're really pushing handsets right now but I still recommend that you bring your own (unlocked) phone.

TIM offers all of its services to pre-paid customers except international roaming. That means MMS and Edge are available (wherever possible).

Prices are in line with the competition and will depend on where you are in Brazil - each State has its own call prices. Two plans available: Meu Jeito, with a choice of different off-peak times (morning, noon, afternoon, you get the idea) plus a single-rate option; and Meu Tempo, where you set the amount you're going to spend that month and can top it up if you use your phone more than you were planning to.

Coverage not as good as the competitors outside large cities.

Extremely obtuse CSR's (took me about an hour of being bounced back and forth across three or four different call centres before I could extract some information from them, things like GPRS and CSD settings). It seems TIM has several customer support call centres across Brazil (I noticed three different accents) and they don't seem to be able to speak with each other, so each time your call is forwarded to somebody else - and that'll happen with alarming frequency - you'll have to explain your request again.

As per Oi: avoid TIM own shops to get your SIM card.
Declare your phone to Brazilian customs to get the infamous little paper slip. Bring passport and other ID with you. And be patient - you'll need to.

CSD and GPRS settings available from this thread.

TIM's main strength is its nationwide coverage, but don't buy into that if you're planning on wandering outside the big cities. Oi Chips are cheap at R$25 and come with some credit, plus the ability to use all available services except international roaming (pointless in this case anyway).

Personally I've had bad experiences with TIM in the past as a contract customer (their billing system played up on me on several occasions) but as pre-paid provider it seems to be OK. Their customer care is chaotic and worse than Oi's (which is pretty bad itself).

Don't expect coverage outside large cities and major tourist spots and you'll be fine.