You can use an HTTPCaller to download the web page and then parse through it. Depending on how it's built this may or may not give you access to the data. Plain HTML usually works ok but dynamic stuff can be a hassle.

A link/URL is fairly simple, but to replicate the action of a button is trickier. Take a look at the source code for the page, then see if the HTTPCaller can be used to replicate it. Like @redgeographics says, you want to hope that they are using HTML and the button has a formaction and formmethod attribute. That you can easily mimic in a HTTPCaller. But if the site uses Javascript or similar then I don't know what you would do.

Just as @mark2atsafe says replicating the action of a button can be tricky. Using developers tools of your browser of choice might provide some insights on what is happening under the hood.