I slipped down a couple steps yesterday. My left foot is swollen tender and discolored on the top. Is it a sprain or broken?

Walk the Walk. Maybe both! If you can walk on it, it's probably a sprain or a small fracture-but if it's swollen and tender and discolored it's a moot point.Go get it examined and maybe x-ray'd.You don't want to walk too much on an injury that looks like that without finding out what's going on inside.Chances are you might get away with it but if after 2-3 days it's not getting better or is the same, see a doc.
A Coin Flip. Swelling, tenderness and discoloration are classic signs of both a fracture and a sprain. The treatment is basically the same. Rest, Ice, Compression and elevation. The only sure way to differentiate between the two, however, is with an x-ray. You can wait a day or two, but to remove all doubt, see a doctor.
Need X-ray to tell. You would need X-rays to determine where or not your foot was broken. If you are not able to place weight on your foot, have a severe limp, or do not see improvement over during the week a physician evaluation would be helpful. A sprain is likely given they are more common.