How can start a new plant from my coneflower (ruby star) plant?

Echinacea isn't going to grow from stem cuttings...

Easiest way is to collect the seeds when they're ripe...

Echinacea seed requires cold stratification to grow...

So... I sow them in the autumn... And they come up in spring.

Some people talk about seeing the broken roots send out new plants when they transplant mature plants.... So... You might try taking root cuttings...

Edit:

Re seeds:

You want to wait till the seeds are mature.

It's pretty obvious... At my house, the birds are eating them all... This year.

It's ok, they drop enough that I'll have plenty of seedlings.

When I plant the seeds, yeah... Fresh seeds... After they are mature... Seems like the stalks turn brown...l I'll clip the stalk, and scatter the seeds over the seed bed... And toss down the stalks to mark the location of the scattered seed.

Leave the seeds on top of the soil.