Fresh plaster is a super-absorbent surface and this can present a problem when painting it for the first time. Because of its absorbent nature, paint doesn't bind well to it and will simply peel or flake off as it dries. In order for your emulsion (water based) paint to adhere to the plaster properly, you're going to have to apply what is known as a 'mist coat'. Luckily, it's really quite simple and you won't be needing any extra equipment or substances such as a PVA primer.
Before you start any of this though, you need to make sure that the plaster on the wall is sufficiently dried. This can happen after just a few hours but it's definitely best to err on the side of caution on these sort of matters so I suggest between 48 hours and a week for most newly plastered walls. There are a lot of variables that can complicate things though such as temperature and humidity as well as the thickness and type of your plaster so you have to judge it for yourselves from the look and feels of the plastered wall. Some suggest leaving plastered walls for much longer and some plasterers even suggest 6 months but this just isn't realistic and I suspect a lot of this is just security so they can shift the blame incase things do go wrong.
So now for the mist coat. This is probably the easiest, cheapest and most effective way to begin painting a newly plastered wall so there's no reason not to do it. Basically, you just dilute your emulsion paint with water to a 50:50 mix as this thiner, watery paint is able to sink into all the tiny holes in your plastered wall forming a secure bond as it dries.
You'll usually get away with just one mist coat but it's worth doing two if it seems like the wall is still too absorbent and the first coat is barely noticeable. One thing to watch out for when painting with diluted paint is how messy it can become. It's much more prone to dripping and I would suggest carefully using a roller and making sure to remove as much excess as possible with the roller tray. Also, you'll need to use a fully waterproof floor protector such as plastic sheeting rather than cotton dust sheets as the paint can go right through the fabric.
It does't matter if your walls are slightly patchy as in the image. This is only the first coat and the important thing is that the entire surface was covered. You're now ready to begin painting your newly plastered walls knowing the paint won't flake off at a later date.
If you're on a tight budget, you can use just a cheap, white emulsion paint for the mist coat and paint over this with a more expensive paint of your chosen colour afterwards. Designer Paint (link in the top right of this page) offer a great range of colours at affordable prices.