Okay, so a while back I broke one of my guitar strings, so I bought a new set. The problem is with my new strings my guitar sounds awful. Like it doesn't sound new awful it sounds like its completely out of tune. Its horrible. I keep checking each string separately and it sounds fine, but as soon as I try some chords its just like nails on a chalk board. So any tips?
My guess is that you neglected to stretch the strings properly. That would account for the general difficulty you're having with getting and keeping the strings in tune.
See the answers to this question for how to do this. There is an important point made that quality strings don't actually stretch when you do this, but the action pulls the windings tighter so less slipping and settling occurs there. It's more cinching than stretching per se. It pulls the slack out of the coils.
Or, it's possible that you've got slippage at the machines. See the answers to this question to make sure your strings are wound good and tight on the tuning pegs in the first place.
And finally, make sure you're tuning up into the note every time you tune. If you go too sharp, you must detune to below the note and try again (and again) to come up into the correct pitch. This makes sure the gears in the machines are locked.
Also, take a look at this question (or this question from Ulf's comment) if you may have changed gauges (sizes) of strings. It may affect your intonation. This will affect your results if you're using the fretboard method to tune the strings by ear. Take a look at this question for more advice on tuning. Short-term you should be using an electronic tuner. Long-term, you might want to look at the answers to this question for techniques of tuning by ear (one by yours truly).
You say "sounds fine". Do you have a digital tuner? If not, download a guitar tuner app on your phone. If you're relatively new to the guitar, my first bet would be that you don't have good enough ears yet to tune by ear. Keep working on it, you'll get there - but in the meantime, a digital tuner will see you right.
My next bet would be that you haven't tuned the guitar to the correct pitch, so it's pitched too high or too low. That'll affect intonation as soon as you fret a string.