Twitter - share button, but with image
Solution 1:
Look into twitter cards.
The trick is not in the button but rather the page you are sharing. Twitter Cards pull the image from the meta tags similar to facebook
sharing.
Example:
<meta name="twitter:card" content="summary_large_image">
<meta name="twitter:site" content="@site_username">
<meta name="twitter:title" content="Top 10 Things Ever">
<meta name="twitter:description" content="Up than 200 characters.">
<meta name="twitter:creator" content="@creator_username">
<meta name="twitter:image" content="http://placekitten.com/250/250">
<meta name="twitter:domain" content="YourDomain.com">
Solution 2:
To create a Twitter share link with a photo, you first need to tweet out the photo from your Twitter account. Once you've tweeted it out, you need to grab the pic.twitter.com link and place that inside your twitter share url.
note: You won't be able to see the pic.twitter.com url so what I do is use a separate account and hit the retweet button. A modal will pop up with the link inside.
You Twitter share link will look something like this:
<a href="https://twitter.com/home?status=This%20photo%20is%20awesome!%20Check%20it%20out:%20pic.twitter.com/9Ee63f7aVp">Share on Twitter</a>
Solution 3:
You're right in thinking that, in order to share an image in this way without going down the Twitter Cards route, you need to to have tweeted the image already. As you say, it's also important that you grab the image link that's of the form pic.twitter.com/NuDSx1ZKwy
This step-by-step guide is worth checking out for anyone looking to implement a 'tweet this' link or button: http://onlinejournalismblog.com/2015/02/11/how-to-make-a-tweetable-image-in-your-blog-post/.