How to save money in the USA

Services in USA are very very pricey. To that extend that it makes sense to fly to the other continent to see a dentist. You would save money already!
In every day life however, we spend money mainly on food and transportation. Check out the stores near you and find out which supermarket sells your favourite food for less. I noticed that milk and eggs are much cheaper in a certain German supermarket than anywhere else.
Public transport is not well developed here. It doesn't exist in vast areas of the country. But near big cities it might be an option for you. It is not very cheap or convenient but might be your only option as parking in big cities might cost more than trip there and back by metro or a bus.
Then there is a free transport available countrywide but not all like to pedal in snow or scorching sun.
If you have a car you can also save a lot on gas if you know where to buy it. Sometimes price might vary by 30-40 cents per gallon (that's about 20%) within a kilometre or two!
Cellphones, internet and cable TV are also very expensive here. Most Americans have unlimited this and that on their phones but they pay 60-80 dollars a month. You don't have to. If you are new to the country and have no friends or family here you won't be on the phone all the time. Check online for prepaid services. I spend about 3 dollars a month on my texts and calls.
Most Americans live in suburbia. There might be only one provider for internet and TV there so you are looking at the cost of $80-200/month. For that reason I only subscribed to the internet and watch movies and shows on Netflix. If I really want to watch a regular old fashioned TV, get an aerial antenna and do it like 50 years ago. Those are free, you just need about 50 bucks for the antenna.

I will suggest to use the Mint app for iPhone. It's helping to manage the budget and see expenses.