You can buy tickets at outlets around the city, or on the transport itself. Trams are good for the inner city, buses go farther out, while the metro is most useful for getting to the international bus station. Driving in the city is actively discouraged, and there's absolutely no free parking in the canal zone. If you don't buy a parking voucher you'll be wheel-clamped. It makes more sense to park outside the city and come in on public transport.
Motorcyclists can park on the pavement free of charge.
Amsterdam taxis are among the most expensive in Europe. It will cost you no more to call one than to hail it, although in theory you aren't supposed to pick up a cab on the street. Amsterdam has 550,000 bicycles and this is an ideal way to get around, although you need to get used to the idea of having your bike stolen. If you're going to be around for more than a month, consider buying a secondhand bike, and make sure you buy a lock as well. Amsterdam, A Short History by Dr Richter Roegholt provides a good, concise summary but few insights.