One of them is a pure carbon tax on all carbon emitting sources, which is regressive: it will affect poorer people more while affluent people can just conveniently pay more to emit the CO2 they need.
The other way is by specifically increasing taxes on income and wealth and using that money to invest in decarbonisation - for the most part by making solar, wind (and in some cases nuclear) cheaper, which eventually makes carbon more expensive in relative terms.
Governments these days tend to focus on the second way, either because it's progressive and therefore perceived as fairer, or because they see the alternative as political suicide (Macron's Gillet Jaunes appeared because of a proposed carbon tax on petrol)
This already exists, but the problem is that carbon credits are nearly impossible to regulate (it's very hard to prove that some carbon-reducing initiative isn't counted toward two distinct carbon credit programs or that the carbon is even reduced as promised). It's hard to do the accounting correctly for honest participants, which pretty much guarantees fraud among less honest participants.
However, come to think of it, one might want to give everyone some carbon credit or travel points, and then develop a market in it. (That would still mean that the rich will fly as much as they want, but at least they'll pay the poor that don't travel for the privilege.)