New strings need to be properly "stretched" when they are put on, otherwise they will get out of tune almost immediately. They are wound really tight and pulling them just a little bit will stretch them out a bit and if they were in tune but got stretched they will get out of tune.
So when you are putting new strings on, tighten the string on about half way, then use your thumb to hold the string down at the first fret and the other end of the string should be held by the bridge (where you put in the strings), then with your right hand pick up the string in the middle somewhere near the 12th fret and pull it up to "stretch" it... repeat this a few times and the string will get stretched and will be properly worn in so when you get it tightened it won't go out of tune when you're playing. Make sure you don't pull too hard when stretching it, it doesn't take much, you just need to pull it a little
If they are already on your guitar you can just play the guitar until the strings get stretched on their own... this could take between 1 week or maybe a whole month (depending on how often you play), or you can just loosen the string a bit and stretch it then re-tighten it >.<
The strings might be breaking easily because they are the wrong gauge for you, there are lighter gauge strings (these will be easier to strum through, they will give in to a pick easier and be easier to fret) and heavier gauge strings (these will give more resistance). If you have really heavy gauge strings but are trying really hard to put the pick through the string, they might break. You can try for some lighter gauge strings or you can adjust your right-hand technique (you will want to work on your picking and strumming in such a way that you glide across the strings, as opposed to fighting to get through them). Or maybe you just have light gauge strings, and these are by nature weaker and break easier, so you might need to get heavier gauge strings. Typically, if you want to play hard rock music, you will want heavier gauge strings, and if you want to play softer stuff or a lot of strumming you will use light gauge strings. Let me know if any of that helps, if not there are other possibilities, just ask me and I'll go in depth of those >.<