Hi,
These companies will most likely expose a Web Service you can connect to. You ask this web service for information, and will most likely need to provide parameters such as a tracking number.
If those companies do not give public access to their tracking system (for example, its only available via their website) then there is little you can do.
I googled 'UPS web services' and found this:
http://www.ups.com/content/us/en/tracking/tools/index.html
FedEx have a developer's centre:
http://fedex.com/us/developer/
TNT I can see nothing obvious.
DHL:
http://www.dhl.com/publish/g0/en/eshipping/webship.high.html
The general principle is you use their publicly available web services in your website to access the information you require.
It may not be a web service, they may give you a widget, or a JAvaScript API or some other means to programmatically access their data.
HTH,
Adam