The cost of living in Helsinki is high, especially as compared to Central Europe. Your rent will be the primary contributor, but groceries and entertainment expenses are also higher. As with any city, you can control your spending, but only to a certain degree - I would recommend making a conscious effort to save before going on exchange, so that you can enjoy yourself without worrying too much about funds.
There are basically two types of accommodation in Helsinki: student-specific housing, and regular apartments/room rental. If you apply to UniHome for student housing, the rent can be anywhere from €390-600 - this is a really good deal for Helsinki. The other option is Hoas whose range is much broader, anywhere from €300 to over €1000 per month.
On average, a normal rental will cost between €450-700 if you’re sharing, or at least €900 for a studio or one-bed apartment. On top of your rent, expect to pay around €100 for utilities for the entire apartment. While heating and water are often included in the rent, internet and electricity are not.
Groceries are another area where it’s possible to spend big - however, unlike accommodation, you have much more control over this area. It mostly comes down to your priorities; if you’d rather have a minimalist diet and focus your finances on socialising, or a particular hobby, then that’s your prerogative. However, I wouldn’t expect you to get by for less than €150 per month.
There is an abundance of supermarkets around Helsinki, so shop around at different stores for the first few weeks to get an idea of prices. Soon, you’ll know where to go for your meat, tins and fresh fruit and get the best price for each! The most popular "budget" supermarkets are Lidl, Sale, Alepa and K-Market.