Q:

Overriding styles without !important

How is it possible to override styles specified in another style sheet? 
I do not want to use the !important tag to override them. I would much rather specify a new style sheet, put styles in there. Could this be achieved by changing the load order of the style sheets?

A:

It depends. CSS stands for Cascading Style Sheets, and there's a specific order that styles are applied in, overwriting previous styles. Without going into too much detail:

If your rules have the same specificity, just load your stylesheet second and everything will work fine.
If your rules have higher specificity, the order won't matter.
If your rules have lower specificity, you'll need to modify them to match.

So, what's specificity? Basically, it's the sum of each selector in a rule. So this:
a {
    background-color: black;
    color: white;
}

Has less specificity than this:
body a {
    color: orange;
}

ID selectors have higher specificity than class selectors, which have the same specificity as pseudo-class selectors, which have higher specificity than tag selectors. So if all your content is contained in a <div> with an id of content, you would be able to override a style that looks like this:
body a {
    border: 0;
}

With:
#content a {
    border: 1px solid black;
}

