You want to make sure your stylesheet comes after the other one when you write it in your document. Also, IDs have higher execution priority than classes. That means p#love styles will win out over p.hate. Specificity will also play a part, so if your element is not displaying the style you want, maybe it's because the other stylesheet has more specificity. For example, .container p.intro will have priority over p.intro, and #maincontent p.intro will have priority over .container p.intro. So check how each element is nested and you'll be able to track down your problem.
I read in Eric Meyer's book that you should think of IDs as hundreds, classes as tens, and tags as ones. so #maincontent p is 101 while #maincontent p.funky is 110 and #maincontent .love p is 111.
Outside of a dog, a book is man's best friend. Inside of a dog it's too dark to read. Groucho Marx