Changing the default application for most files in OS X is easy. OS X also allows you to choose your default web browser and email client, but these options are hidden in a place you might not expect.
Some browsers and email clients may offer to automatically become your default when you first launch them, but if they don't--or if you want to change it later--you'll have to find OS X's settings for these.
How to Change Your Default Web Browser
To change your web browser, you'll need to use the System Preferences window. To open it, click Apple menu > System Preferences.
Click the "General" icon at the top left corner of the System Preferences window.
Click the "Default Web Browser" box here and select one of your installed web browsers.
If you don't see a "Default Web Browser" option here, you're likely using an older version of Mac OS X. On OS X Mavericks and earlier, the option to change your default web browser is located in Safari's preferences. Launch the Safari browser and click Safari > Preferences. Click the "Default Web Browser" option under the General tab and select your preferred web browser.
Choose Your Default Email Client
To change your default email client, you'll need to open the Mail app included with your Mac and change your default email client from there. Yes, this is a bit weird--you need to use the default Mail app to change your email client even if you don't want to use the Mail app for anything else.
First, open the Mail app. If you don't have its icon on your dock, you can press Command+Space to open Spotlight search, type "Mail", and press Enter. You can also open a Finder window and head to Applications > Mail.
Click Mail > Preferences to open the Mail app's preferences window.
Click the "Default Email Reader" option on the General tab and select your preferred email application.
Applications only appear in these lists if they're installed, so you'll need to install a web browser or email client before it appears here.