If you are a tourist, as a general rule, you won’t need to use your car or a bus to get around Verona. The central part of Verona is relatively small and you can reach everything on foot. If you decide to visit the lake or the rest of the area around Verona you will need to use public transportation or to rent a car (or to use your own car if you have one with you).
The lake is easy to visit if you have a car. The lake is really huge and you can’t walk from one place to another. If you take a bus from Verona bus station (in front of the train station) the bus will take you to one of the towns at the lake but you’ll need to get another bus in order to move to another place and this will take a lot of your time. One solution would be that of renting a car. Another solution would be that of taking a bus or a train to Desenzano or Peschiera and from there taking a ferry that travels around the lake and drop you off where you want.
In Verona your car can be left parked somewhere, but be careful where you park it. Many hotels have parking facilities or discounts for parking lots. If you don’t like to walk you can always use city busses or taxis. If your hotel is in the suburbs you’ll probably need to use a bus or a taxi to get back to your hotel (it depends how far the hotel is, but sometimes after a long day under the sun in central Verona you don’t probably want to walk a long time to get back to the hotel). Some hotels are too far to be reach on foot but they generally offer rides to the centre.
The best thing to do is to plan your tour before departing from you hotel. Buy a map or get a free map from the tourist office and plan what you want to do for the day.