How do you get red orb in Pokemon Heart Gold?

You can only get the Red Orb in Pokémon Ruby; in Sapphire, you get the Blue Orb, and you get it from the old woman at the peak of Mt. Pyre.
You cannot get a Red Orb in Sapphire, as it is available only in the Ruby Version. However, in Sapphire, you can get a Blue Orb which will be at Mt. Pyre's peak, given to you by an old couple there. You can gain access to the Cave of origin in Sootopolis city with a blue orb and catch Kyogre.

But in Ruby, you can catch Groudon instead of Kyogre.

^_^
You can't obtain the red orb in Sapphire.

Team Aqua uses it to awaken Kyogre, while you are given the blue orb in order to challenge it. In Ruby however, team Magma has the blue orb, while you get the red orb to challenge Groudon.

You can't have both orbs (and thus be able to fight both Kyogre and Groudon) on either one game. That's only possible in Emerald version.
Go to the top of Mt.Pyre and it will be there.
You can not find the red orb in Sapphire. You can only find it in Ruby and Emerald.

Well, technically [if I remember correctly] the old woman gives it to you when you go to look for the blue orb. But it is pretty much completely useless in Sapphire.