Whomever told you that looks don't matter is lying. Well, at least if they told you that about resumes. Creating a good looking resume doesn't mean you have to stud it with diamonds and spray it with perfume. But it does need to look professional.
The first step to creating a professional resume is to stick with one style. If you bold the name of one of the companies you worked for, bold them all. It will make you look indecisive or disorganized if you constantly change your style. This also applies to text fonts. Picking the right font can be a tough decision. You want your resume to stand out, but you don't want it to look overly extravagant, either. It all depends on what you are comfortable with, but I would recommend staying away from Times New Roman, the default font for Microsoft Word. It doesn't look the best on-screen, which can make it a little difficult to read. I would suggest using Georgia. It's slightly larger than Times New Roman, which makes it a little easier on the eye. Oh, and if you're thinking about using Comic Sans, think again.
Readability is a key aspect of your resume. We've already gone over how font can affect this, but line spacing plays a big role too. You don't want to double space your text, that will take up too much space, but you will want to implement some spacing. Without it, your readers' eyes will strain quickly. The amount of space you will want to use will depend on which font you chose. If you are using Georgia, increasing your line spacing to 14 points should do the trick.
One final thing you will want to do is to make your resume easy to skim. Hiring managers have thousands of resumes to look over, so it's important to make all of the important information stand out. That means taking advantage of bold and italics to highlight the most important aspects of your resume. You can also implement some fancier techniques, such as implementing borders or shadings to your headers.
Resume design isn't exactly a high art form, but the way they look can have a big impact on how an organization views you as a candidate. Keep this in mind during your job search.