cURL and click a button in a website

Your best bet is to use something like Firebug or the Live HTTP Headers plugin (both are for Firefox) to try actually clicking the button and seeing what is going into the resulting request. Then try to replicate it.

Here's a simple example, though:

a form on a web site:

<form action="http://someUrl.com/somePage.html" method="POST">
    <input type="text" name="value1"> <br />
    <input type="text" name="value2"> <br />
    <input type="submit">
</form>

Typing "Some value number one" in the first box, typing "Some value number two" in the second box, and clicking the submit button would generate a request that looks something like

POST /somePage.html HTTP/1.1
Host: someUrl.com

...//various other POST headers here

Content-Type: application/x-www-form-urlencoded
Content-Length: 57
value1=Some+value+number+one&value2=Some+value+number+two

which would translate into a cUrl command like

curl -d "value1=Some%20value%20number%20one&value2=Some%20value%20number%20two" http://someUrl.com/somePage.html