Something that is very different to most countries (at least in my experience) is that most places, whether it is a restaurant or a store, don't accept VISA and sometimes not even MasterCard. The standard card for dutch banks is Maestro, and if you have this card, you will have no problems in Holland. However, many exchange students constantly have to get cash from an ATM to do groceries and other purchases since they only have a VISA. I recommend to get a Maestro card before going to Holland, unless you want to become the customer of a dutch bank. For my part, I had a Maestro already, which helped a lot.
In general, the prices of most things are lower in Holland compared to Sweden. The main difference I noted was the prices of food, as it can be as much as half the price of what it would be in Sweden. Of course it will vary from person to person, but I kept my costs for groceries between 25 and 35 euros per week.
It is also not too uncommon that some students buy their lunch every day, or most days. In the Medical Center of the university, you can get the "meal of the day" for 3-4 € (generous portion) or buy sandwiches or salads for 2-3 €. A meal outside of the hospital restaurant can cost you 4-6 € for fast food and a meal in the average restaurant costs 6-9 €. One thing to point out is that they charge you for water in most places, so for drinks you usually end up buying something else which can cost you 1-3 € (which would be the same price as taking water).
However, if you want to keep the costs down, of course want to avoid buying lunch every day. When it comes to grocery stores, the cheaper ones you want to keep an eye out for are Aldi, and Jumbo (can be slightly more expensive than Aldi). "Albert Heijm to go" are smaller versions of Arlbert Heijm which can be compared to Pressbyrån in Sweden, more expensive but usually have what you need on the go. There are larger Albert Heijm stores, however, I do not know the price on those but have heard that they can be around average in price. Lidl also exists in Leiden, but not close to the center of the city.
Public transport is something that actually feels MUCH more expensive than in Stockholm. Holland is a much smaller country than Sweden and has shorter distances between cities. They don't have city-bound public transport such as SL in Stockholm, but have one company, NS, which handles trains for the whole country. This of course means that if you have a monthly subscription you get access to the every train in the country, but that comes with quite the price as the monthly (unlimited access) subscription costs 410€ per month. You can get a subscription for 102€ per month, but it only allows you free travel during "off-peak" hours during weekdays and unlimited during week-ends. If public transport is necessary, usually it is cheaper to buy a "Traject" subscription, which allows you unlimited access to the stations you choose for your trajectory (Prices vary for the trajectory). If you travel on cash on the train, and happen to be with someone that has a subscription, often they can give you a 40% discount as you travel together (has to be enabled on a NS charging station).
NOTE: NS subscriptions do not account for the metro, tram and bus as you they are handled by city specific companies (yet can use the same card). To travel with these it is easiest to use travel credit you can charge in any station. Also, subscriptions can only be made on a personal NS card (have to be ordered), not a generic one. As NS trains have 1st and 2nd class wagons, make sure your card is set on 2nd class and not 1st class to make it cheaper (same goes for when you buy a subscription).
Useful Links
NS (Dutch train company) - Note that Trajectory tickets are only visible on the dutch version (translate it with google).
9292 - Popular dutch travel planner. This can also calculate your transportation costs with metro, bus, tram and train combined (and suggest cheapest option possible). App for the phone is available.