#Harry takes a train back to the Dursleys.
Harry takes a train back to the Dursleys.
Once Harry and Hagrid are done buying his Hogwarts supplies in Diagon Alley, Hagrid takes him back to the train station, and gets him lunch before it’s time for Harry’s train to leave.
“The late-afternoon sun hung low in the sky as Harry and Hagrid made their way back down Diagon Alley, back through the wall, back through the Leaky Cauldron, now empty. Harry didn’t speak at all as they walked down the road; he didn’t even notice how much people were gawping at them on the Underground, laden as they were with all their funny-shaped packages, with the sleeping snowy owl on Harry’s lap. Up another escalator, out into Paddington station; Harry only realised where they were when Hagrid tapped him on the shoulder.
‘Got time fer a bite to eat before yer train leaves,’ he said.”
- Harry Potter and the Philosopher's Stone, Chapter 5 (Diagon Alley)
The train Harry gets on would take him back to the Dursleys - presumably not directly to their house of course, but close enough to it that he could find his own way back.
“Hagrid helped Harry on to the train that would take him back to the Dursleys, then handed him an envelope.
‘Yer ticket fer Hogwarts,’ he said. ‘First o’ September – King’s Cross – it’s all on yer ticket.”
- Harry Potter and the Philosopher's Stone, Chapter 5 (Diagon Alley)
Harry gets from Diagon Alley to the Dursleys by taking a train back, and presumably either walks or finds transport the rest of the way traveling back with his belongings.