How to keep a violin in tune?

A few months ago I received a cheap used violin for Christmas. When first trying to tune it, I accidentally broke a string. So finally, a week ago I got around to buying a whole set of strings. When attempting to tune it again, the violin will just not stay in tune. For example, I will tune the "G", and by the time I finish the other three its already F to F#. This is pretty much true for all the strings. I don't know if its the pegs being loose (which they kind of look like), or if the strings just need to break in. I'm new to this so any advice is welcome. Thanks in advance.