As European cities go, the cost of living in Delft is about average, perhaps slightly above average if you choose a pricey flat. As a student or intern in Delft, you’re probably looking at spending of €800-1100 per month. The lower end of that range would be quite impressive, whereas €1100 assumes quite a free, activity-heavy lifestyle.
Your rent will fall between €350 and €700 or so, depending on how lavish or lucky you are. This is the dominant expense each month, so if you are willing to compromise on your flat a bit to save a chunk of money, you’ll be able to reinvest it in beer, travelling and socializing!
In terms of groceries, they are pretty cheap, especially if you go to the open market and buy your fruit, veg and meat there. The De WarenMarkt is a good one, but you’ll find all sorts of markets around the city. I’d estimate €200 per month on groceries if you cook most of your own meals and don’t just eat trash.
Eating out is a different matter, a basic lunch menu could be €13, beer is €3-4 and a quick sandwich will be €3-5. They aren’t crazy prices, but if you regularly eat on-the-go or go out for dinner, you’ll need a more generous budget than most students. You can always get a part-time job to supplement your income (you’ll need a work permit if your home nation is outside the EU/EEA) and live a little more lavishly.
Paper tickets for the public transport in the Netherlands have been abolished for a few years now, and almost nobody in Delft buys single tickets for journeys. Once you arrive, the popular public transport option is to grab an OV-Chipkaart, basically a Dutch travel card that’s valid on all forms of transport in the country. You need to have a €20 minimum on the card, but since Delft is quite small you’ll probably just cycle most of the time anyway.
You can buy a second-hand bike in Delft for around €50-100 if you shop around online or through your university. There is also a "free" student travel card that you’ll hear about when you arrive, but this is not available to international students. The reason isn’t discriminatory, but that they aren’t actually free - taking one out affects the student loan for domestic students. Sorry, but you’re gonna have to pay for that bus!