Why does IE not read CSS correctly? How can it be fixed?

So I'm just coding a simple little site in CSS, and I'm checking all of the popular or known browsers when I come to Internet Explorer. I used the rule border: 1px solid #424242; and rounded it off, with border-radius: 10px (or 10px 10px 10px 10px in some cases); and while the border was there, the corners were not contained and could be seen outside of the border. The search, while nestled neatly in the right corner of the navbar in the other browsers, was somehow below the navbar. There's more but those are just examples. Any way I could fix them or is their a site that helps to overcome IE problems?