I dug this out of an old project and thought it'd be worth saving. I remember back then having real issues trying to find example code.
I did have a quick google and found InstapaperXAuth by Kin Lane but as the link says, it's a stripped down version of a Twitter OAuth package. This project is custom built just to work with the Instapaper API, so it's only a handful of lines long.
<?php
require 'src/instapaper_xauth.php';
$insta = new Instapaper_XAuth("CONSUMER_KEY", "CONSUMER_SECRET");
var_dump($insta->login("USERNAME", "PASSWORD"));
All you need to pass in is your consumer key + secret, and the username and password of the user you want to authenticate as.
If the credentials are valid, you'll recieve an array with two keys, 'oauth_token' and 'oauth_token_secret'. These can be used to make normal OAuth requests.
This library is so small because it doesn't handle making requests to the instapaper API at all. I personally like using OAuth in PECL for all of my OAuth related needs. Here's an example of how to verify your credentials:
$api_url = 'https://www.instapaper.com/api/1/';
$oauth = new OAuth("CONSUMER_KEY", "CONSUMER_SECRET", OAUTH_SIG_METHOD_HMACSHA1, OAUTH_AUTH_TYPE_URI);
$oauth->setToken("OAUTH_TOKEN", "OAUTH_TOKEN_SECRET" );
$oauth->fetch($api_url.'account/verify_credentials');
echo $oauth->getLastResponse();
There we have it, a request to the Instapaper API in just 6 lines of code :)