What is the continuation after the last episode of Naruto Shippuden? After the last episode of Naruto Shippuden where Naruto and Hinata are getting ready to get married and ends right there, what's after that?

Is there a movie or does it go into Boruto?
There are 2 movies after the end of the series.

The first one to watch if you are interested in knowing things that happen before the marriage that is is preceds the last few episodes is The Last: Naruto the Movie


The other movie is Boruto: Naruto the Movie which covers the Chunin Arc of Boruto series and has an anime adaptation as well. Personally speaking I like the anime adaptation better especially due to the better art work on the villains. 

You can also watch Boruto Anime directly you most probably won't have any problems in understanding it except that a character that appears many a times in Boruto's dream is a character from the movie The Last: Naruto The Movie.

There is an OVA as well about the day Naruto became the Hokage titled The Day Naruto Became Hokage (OVA)
It was included on Limited Edition CDs and Blu-ray releases of the Boruto movie