Nearly every application has a Preferences menu. Just click on the application's name at the top left of the menu bar next to the Apple menu. This is called the application menu, so when someone says to click on the application menu, they mean to click on the application name in the menu bar.
From there, click Preferences. This is where you can set all your preferences for any particular program. Click the Advanced tab and next to Accessibility, you'll see a check box with "Never use font sizes smaller than" and a drop down menu where you can choose the smallest font you want to deal with. Check the box, choose a size and you're all set.
One cool feature I really like in Safari is the Reader. It doesn't work with every site, but it does with most sites. Basically, it isolates the main text of a page away from the ads, links and sidebars that sometimes clutter a page. When you click reader, the extraneous information disappears leaving only the article text in easy-to-read font. Click the Reader button again to return to the normal appearance.
