unless they also offer a javascript-based method where you just include their javascript and it displays the data, you'll have to get into some server side language. While being a great opportunity for you to learn something new, if you want to save the time, ask them wether they can provide you with a snippet in whatever language your host offers.
Do you want to include it on every page or just on your home page?

I have a page which is basically a /weather expansion of the webpage I currently have online.

They don't offer a javascript option but told me that php or another server side language could be used to display the information in a web displayable format.

SO it looks like I will have to hire a coder to do this for me?

hiring a code is the easiest way.
If they provide a sample-script, the coder would just have to install it and may be tweak the layout a little so it fits your page, which shouldn't take too long.

could I get an idea of how much a coder will charge for a job like this?

That depends on where the coder is located and how much he's charging per hour. And it depends on wether they can provide you with a sample application he can just push in, get your layout, put it around that and be done. If that's the case (and there won't be any unforseen problems with your server not supporting something that is required, check that with your support before you start looking for coders, also, check which languages you can use), it shouldn't take more than maybe an hour, probably less.

if they have a sample and you're ready to get your hands dirty just a little bit, I'm pretty sure you could do it yourself with a little help from the guys here at webmasterworld.com.

So, whatever you want to do, here's what you need to do first:
Ask your webhost which server side languages they support.
Ask the service for a sample implementation in one of the supported languages.
It's possible your webhost tells you that you need to upgrade your account so you can run server side programs, in that case costs will probably increase.

My webhosting package is not a problem.

I have support for phpbb, perl, cgi etc with unlimited databases so I am pretty sure that my server will support it.

An example of implementation 7 day forcast information is on a rival site in php is @ <snip!> minus the satellite images and hurricane watch images.

no upgrades to my server necessary and the only cost will be for the programmer.

[edited by: httpwebwitch at 7:06 pm (utc) on July 24, 2008]
[edit reason] url removed [/edit]

Sorry I wasn't clear on that. I meant the source code, like, a script that implements the process. Having that would make it easier. Without it, it may range from one hour to several hours, depending on the skill level of the programmer, the complexity of the service and your wishes.