How to Purify Water?

During these so very dangerous times, I've read that it's advisable to have emergency supplies and to stock up on food and water and my family has taken this to heart. I've gotten the food part of it down, but how do I store drinking water so it'll keep safe to drink? Will I have to buy ready-made bottled water or can I bottle it myself and what would I have to do, if anything, to treat the water to keep it safe over a period of time? We don't have a yard, so a well or barrels for storage are not an option unfortunately.

We have a small stream running through the woods at the back of our house. In a worse case scenario, would I be able to make this water safe for drinking? I know you can buy some water-purifying tablets, but they are very expensive here in DK, so is there any thrifty way of treating or cleaning the water myself? Would filtering and boiling be enough?

Vicki from Copenhagen, Denmark