Film Canon
In the film adaptation, Hogwarts has an enormous Clock Tower in the centre of the main courtyard. It seems to chime on the hour and half-hour throughout the day
Book canon
They have clocks on the walls
The following week dragged by. Wednesday night found Hermione and Harry sitting alone in the common room, long after everyone else had gone to bed. The clock on the wall had just chimed midnight when the portrait hole burst open. Ron appeared out of nowhere as he pulled off Harry’s Invisibility Cloak. He had been down at Hagrid’s hut, helping him feed Norbert, who was now eating dead rats by the crate. - HP:Philosopher's Stone - Chapter 14
and upright clocks
‘No, no, no,’ said Hermione. ‘No, we’re not. Why don’t you go to bed, Neville?’ Harry looked at the grandfather clock by the door. They couldn’t afford to waste any more time, Snape might even now be playing Fluffy to sleep. HP:Philosopher's Stone - Chapter 16
Presumably these clocks are literally clockwork, which wouldn't be affected by magic restrictions on electronics.
Our three heroes wear wrist-watches
- Ron:
‘Nearly six,’ said Ron, checking his watch and then staring down the drive which led to the front gates. ‘How d’you reckon they’re coming? The train?’
- Harry:
Harry crept past them to the portrait hole and waited for a minute or so, keeping an eye on his watch. Then Hermione opened the Fat Lady for him from outside as they had planned. He slipped past her with a whispered ‘Thanks!’ and set off through the castle.
- Hermione:
Hermione was tugging at his sleeve, staring at her watch. ‘We’ve got exactly ten minutes to get back down to the hospital wing without anybody seeing us – before Dumbledore locks the door –’
For the record, there are also magical watches (Dumbledore has one) but the rest of the characters seem to rely on mundane clocks and watches
Professor McGonagall pulled out a lace handkerchief and dabbed at her eyes beneath her spectacles. Dumbledore gave a great sniff as he took a golden watch from his pocket and examined it. It was a very odd watch. It had twelve hands but no numbers; instead, little planets were moving around the edge. It must have made sense to Dumbledore, though, because he put it back in his pocket and said, ‘Hagrid’s late. I suppose it was he who told you I’d be here, by the way?’