How do you test an MVP?

There are many techniques you can employ to test your MVP, but the first step is always the same: You need to create a list of hypotheses that you need to validate before you jump into any customer research or testing effort.  A hypothesis is anything that you think is true, but don't have hard facts or empirical evidence to prove it is true. 

Once you have a list of hypotheses you can think about ways to validate them in the field.  Some hypotheses can be tested via good, old fashioned primary market research: Interviewing customers.  You would want to bring the MVP (the smallest possible thing that allows you to complete one build-measure-learn cycle) - in many cases this might be a printout or a landing page or some mockup of what a software interface might look like. This is called a "stimulus" in primary market research. You can take this to a customer, and talk through the product to get a sense of what the customer thinks of your current idea.

This method works well when you are testing just the product concept itself and gauging interest / getting a sense of relative importance of features / trying to understand the end user's mindset and workflows.  This is not a great way to test a business model. To test the economic viability of a product, you need to either charge money by making an outright offer and close a sale (thus proving the customer's willingness to pay), or get a sense of their strong interest by closing a pre-sale.  A landing page test is a very effective way to test purchase intent.