How can I build an email list for my internet marketing business?

The fastest (and least ethical) way is to buy a list. There are a lot of different kinds of lists you can buy, from a cold list of decision makers in a particular industry, to user lists from a competing company, to member lists of various trade organizations.

The best method (and the slowest) is to build it yourself through a subscription model. This is the standard inbound marketing methodology, where you create useful content targeted to your target consumer, and encourage them to subscribe in order to receive still more useful content.