As described on the twitter page, here are the basic pieces you need (note that there is a typo on the twitter url they have on their doc page):
So, if you are constructing the strings for the urls dynamically, make sure and use the string representation of the tweet's id.
You can see it in action by watching the Vine map visualization, and clicking on one of the Reply/Retweet/Favorite links that are to the right of the Vine video. You will be prompted to log into twitter if you're not already, and you get a final chance to confirm the action.
|Real-Time Searchable Twitter/Vine Map, with Twitter Interaction (click image to go to map)|
Obligatory cat included in screenshot.