First, there are 2 types of fonts. Serif fonts and SanSerif fonts. Serif fonts are fonts that have those “edges” and san serif fonts are those without. A good example of a serif font is New Times Romans while Verdana is a san serif.
If you look in your WordPress Theme Stylesheet, you will most probably see the type of fonts the designer has opted to use in the first line of codes. It will be declared with something like this or similar to this:
font: ‘Verdana’, Tahoma, Arial, san serif. OR font: ‘New Times Romans’ Georgia, Times, serif
Wordpress will use the first declaration which is Verdana in this instance and if some of your reader’s computer do not have that font, it will move to the next and next. If for some reason, all the fonts are not available in their computers, then WordPress will use whatever san serif fonts it can find. This is highly improbable, but do remember than there are also many Mac users out there. They might have the same fonts, but Mac fonts sometimes have different names. So it is important to have the denotations serif or san serif properly declared.
There is also something known as web safe fonts. These are fonts that are deemed to be safe for use as Macs and Windows will have these fonts installed by default. Most designers goes along with this safe route to avoid any incompatibility.
So to change the fonts for your Theme, all you have to do is to change the the font names to the fonts you want to use. You can also have different fonts for different areas. For example if you want to use Verdana for your contents and Georgia for your sidebar, all you have to do is specify them individually. If there are no specified fonts for specified areas, then the default font will be used site-wide. It is easy to spot out the fonts as it will be clearly written out in your stylesheet and it is almost impossible to go wrong.