When building for websites you want to make life as easy as possible for you.
There are many tools out there that help make that process easier for correcting browser and function issues.
Firstly I do all my development on Firefox due to it large range of addons.
Tool: User agent switcher
Used for: Making it seem like your brower is a mobile device (iPhone, Andriod, Blackberry etc)
Import: http://techpatterns.com/downloads/firefox/useragentswitcher.xml (used to update your agent list)
Used for: Resizing your screen to see how your website is viewed on a mobile screen
Add: http://resizemybrowser.com/ (additional sizes options for more mobile screens)
Used for: Quickly measuring the size of something on a website
Tool: Total Validator
Used for: Validating your websites html
Used for: Hooking Fiddler to your browser
How to view addons on the browser:
After installing an addon, it isn’t always shown. Right click on the top of the browser and select the addon you want or the addon bar.
Used for: Seeing and editing the redirects of pages and resources.
Used for: another method to view your site on a mobile device screen (beware that you should use the same browser as the mobile for more accurate results)
All other browsers:
IE, Chrome, Safari etc
So with this list of tools you should have everything you need to check and correct how your website will be displayed to your users.