The internet and e-commerce has changed the way almost every company does business.
One of important reasons for this is that information has now become easy to access and the information asymmetry which existed earlier and benefited a few companies while harming the others has been eliminated to a large extent. For example, it has now become easy for even a small company with limited resources to find out where it can buy its raw material at the cheapest rate and sell its finished products at the highest rate.
The ease with which information can be transferred has also made it easier to manage different aspects of business like distribution and sales, control of logistics, inventory management, etc.
E-commerce has made financial transactions easy to carry out. Earlier, financial transactions were carried out using notes or instruments like checks, drafts, etc. These had to be physically carried and the verification process was a long drawn one. Now money transfer over the internet has made the transfer of money easy and has decreased their cost to a large extent. This has opened avenues for many businesses to offer their services over the internet and attract new clients.
This depends greatly on the type of business that you are asking about. For example, the Internet has dramatically changed the way that companies in the music and film industry do business.
For these industries in particular, the Internet has made it much easier for products to be distributed. It has resulted in both legal distribution (Netflix, iTunes) and illegal distribution (file sharing). Both have changed the way that these industries do business. For example, the music industry has gotten away from their emphasis on physical media. They have stopped selling as many CDs and have gone more towards selling downloadable files. This has lost them a fair amount of money and so they have also increased their emphasis on artists' concerts. This has become a big money-maker for them where tours used to be just a way of promoting an album.
So, in the case of this sort of industry, the fact that their product can easily be distributed over the Internet has changed their way of doing business considerably.