Really, going into the future is easy. Seeing as we're ALWAYS travelling into the future, all you'd have to do is be put in stasis until the time you want to go to. Then, if you have the power to go back in time, which would be a separate technology, you could go back to your "present" time.
I noticed in PoA that apparently the FIRST-mentioned future Harry and Hermione didn't successfully release Buckbeak, because he died the first time around. There WAS at least an attempt to free him, though, because of the rocks being thrown into Hagrid's hut and (present)Hermione hearing the snapping of twigs behind her. I used the phrase "FIRST-mentioned" future H&H because it's possible that this was a long loop that happened until they got it just right. Buckbeak was being stubborn in the final attempt, but this time they finally lured him to safety.