I've recently acquired a 45l tank. Set it up for a couple of weeks then added four platys from p@h. they've been settling in OK. I got them a week ago.

But then I read up on fish care and saw about the cycling of the tank. I had no idea about this as p@h just advised to run the tank for a week or so before adding any fish.

I bought the api test kit today and checked the water after cleaning the tank this evening. Here are my readings -

Ammonia 0
Nitrite 0.50
Nitrate 10

I know I have to get nitrites down to 0. But how? Do I have to keep doing water changes until it's down? Thanks

Yes water changes are the answer. Change 60% to get it to a safe level, then repeat whenever necessary until the tank cycles.