The solution suggested by Grzegorz is deprecated and it's not really the best way to do it. For Facebook, you just need to load the JS SDK ( https://developers.facebook.com/docs/reference/javascript/ ) and call the UI feed method on click on your custom button. More details on the UI method: https://developers.facebook.com/docs/reference/javascript/FB.ui/
For Twitter: https://dev.twitter.com/docs/tweet-button#build-your-own
You will have other options for LinkedIn, Google+, etc. but I don't know them from the top of my head and not sure if of all them offer alternatives.
Keep searching, you probably just didn't dig deep enough, it took me 2 minutes to find the link for Twitter :)
