Run at a decent frequency - minimum a train every 15 mins off-peak, every 10 if possible. Peak every 3-5 mins.
Run expresses from first to last train, this is put to great effect in Sydney but prior infrastructure needs to be completed beforehand. E.g. main routes are minimum 4 tracks, some 6. Dedicated freight lines also help so they don't conflict with passenger services. What I like is that Cityrail isn't afraid to run an almost empty all stopper next to an almost empty express.
New lines to be done with metro. They seem to be better than trains as they can run every 2 mins, compared to trains would be hard pressed to run every But the main point is that it is faster than even express trains, meaning you can have way more stops but still be competitive with time. Nothing tells me that I should drive than seeing trains fly past my station due to it being classified as a "small station"
Suburban interchanges - not everyone wants to go to the city so it's important to provide interchanges in the suburbs. Sydney is terrible at this, for example there needs to be a Hurstville to Macquarie Park line. There is not so two of the most congested roads follow this path because there's no option but to drive.
Station integration - connecting directly to places of interest like shopping centres. And over station developments. Density helps a lot too.
Get rid of car centric suburbs - many stations depend on park and rides which decentives public transport use.
Better integrated transport. For example trams, they have their use on street in the city where the stops are closer and it already duplicates a faster line, but once it is out it should be running on dedicated tracks so they don't need to stop at traffic lights. Similar to parts of L1 and soon Parramatta light rail in Sydney where it is completely segregated with other traffic.