For Lean practice, what techniques are used for defining customer value and how is the information recorded and presented?
Value is the high quality outcome of an organisation that the customer is willing to pay for.
there is a difference between output and outcome. The output is the product, the service etc. your company is providing. The outcome is the positive difference the outputs make
the value is always looked from the customer's perspective
Companies measure 'value' in different ways. I've seen places that boil everything down to cash values and some where 'T Shirt sizes' or relative estimates of value are used.
There's nothing wrong with any of these approaches. The important thing is that there is enough granularity in order for you to make decisions and that it's consistent across products/projects/features in order for you to be able to compare them.