How do I tell if my 2001 330ci is a sport package or any other package they offered?

Sports packaged cars have
1. 17" wheels and the car is lower to the ground than a standard car
2. Bolstered seats w/ thigh support (multi-adjustable sport seats)
3. Performance tires,
4. Stiffer suspension tuning
5. 3-Spoke steering wheel w/ controls.

and if you end up getting the car, welcome to the E46 community! haha You should join www.e46fanatics.com should you have any other questions, problems, advice, etc.
good luck with whatever you decide!
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In response to Snowie, actually my 328ci sits on stock 15" directly from the dealership. So that completely debunks your statement, "328ci can't sit on 15" because their brakes are too big."

The only brakes that are "too big" for the stock setup would be from aftermarket brakes, and it wouldn't be the brakes alone, it'd actually be the rotors + calipers.

My current setup with my M has a Big Brake kit from StopTech 380mm (15" diameter rotor), which required me to upgrade my wheel and rim size, because my stock wheels were too small to wrap around the new rotors. the only size rotors you can wrap STOCK M3 rims/wheels are the 13" Rotors and you'd have to buy 3mm spacers along with that kit.

Actually, the previous answer is not too accurate.

The 330ci came with 16" wheels with all-season tires as base model, and sports package gets you 17" wheels with summer only tires. 15" wheels won't fit the 330ci or even the 1999/2000 328ci because their brakes are too big.

You also get sports seats with an adjustable under-thigh cushion and a more fitting side cushion.

A 3 spoke multifunction steering wheel completes the package.

All 2001 and newer coupes came with sport suspension as standard whether you had sport package or not.

The easiest way is to get your VIN number and go to any BMW dealer. They will be able to get you the full info for free.

As a simpler answer, if the wheels are 17 inch M rims, and if the car has a 3 spoke steering wheel, then it has the sport package.