Write on a show.

Be good at it. Be professional and reliable.

Get a producer / co-producer / exec producer / consulting producer credit due to your contribution (or as part of the deal that saw you write on the show in the first place).

Then when the person running it steps down to go do movies or create his own vampire cop show or swim in the lake of gold that the rival network are offering him, get asked to take over as showrunner.

Alternatively: create the show yourself and be attached as show runner.

Alternatively: have done good work on another show and then get asked to join a show and showrun it (could be the original writer hasn't worked out / gone power mad / had a better job offer).

The job of the show running is changing though- as more and more top actors and big name directors move to television, it's starting to mutate more into a mini-Hollywood - where the writer starts to slip down the ladder again. We're not there yet - and won't be for a number of years, but it's definitely changed in the past decade.