One of the many questions you should ask before starting a web project is, will my website work on all devices, and will this cost me more?
As all things related to the internet, website development is constantly changing. However; as technology moves forward, new standards are developed to establish common grounds and expectations. If this was not the case, the internet would be the wild west. although at times, it still feels that way.
One of these recent standards has been the expectation that your website needs to work on all devices (iPhone, iPads, other smart phones and tablets). Align with the embracing of this standard comes the question of what is the most effective way to accomplish this. As with most solutions, it always depends on the details of the problem, but the consensus points to a "responsive approach"
A "responsive approach" means that your website will be planned and developed with one main screen in mind (desktop, phone) first, then for the rest of the screens, the content will be moved, resized or even be removed to accommodate this new screen size and enhance the experience of the user.
Now, that you know the best approach to how your website should be built, the next question should be, will I be paying extra to ensure this is the case?
The answer will depend on the approach that the web development company (namely the developer) will take. If the developer has embraced the "responsive" approach to coding your website, then you shouldn't have to pay any extra. It should be built in in the process.
If in the other hand, the developer is used to coding for only 1 screen and sees any additional screens as additional tasks, then it will most likely cost you more, since the developer sees the a project with separate pieces and not as a single project with specific requirements.
It is very important to understand the approach that the developer intents to take to build your website to make sure you are getting the most for your money.