What would the full hypothetical Mars terraforming roadmap look like?

Really great answers as to the "how". The one thing that must come before any inserted gases is a magnetosphere. Otherwise most of the new gases will be carried along with solar wind.

I know it sounds like 1950s sci-fi, but a viable low-tech solution would be domes and tunnels. Once humans have a solid footing on Mars I would expect the new Martians would naturally improve all aspects of thier habitat.

It's a bit of a late answer, but most proposals don't actually use increased CO2 to warm up the planet. They use super-greenhouse gases (like perfluorocarbons), or they increase the amount of sunlight hitting Mars.

As for a terraforming roadmap, there's one by Robert Zubrin, which proposes that it would take about a thousand years. However, others argue that it would take thousands of years. Making an atmosphere breathable to humans appears to be the most time-consuming step. The earlier steps (warming up Mars, thickening the atmosphere etc.) would be comparatively short, taking a century or maybe even just a few decades.

Personally, I doubt that such expensive and time-consuming projects would ever be performed. I think a more realistic approach would be a compromise: rather than making at atmosphere breathable to humans, it would be more practical to aim for an atmosphere that can support plants. Plants can tolerate less oxygen, lower atmospheric pressure and higher CO2 than humans can. Some animals might be able to survive in this atmosphere as well. Humans would need to live in sealed habitats, but those habitats would be much easier to construct than on the present Mars, and humans could go outside with just an oxygen mask. This kind of terraforming could potentially be completed within a human lifetime. But it's questionable if this could even be called "terraforming" anymore*, and of course it would still be more expensive than any project that humanity has done to date.

One hypothetical roadmap might be this:

1. Study every aspect of Mars extensively. This is necessary for terraforming to have any chance of success, and also to leave a record of the original Mars.
2. Test the terraforming techniques extensively, in Earth labs simulating Martian conditions, and also in labs on Mars itself (carefully sealed off from the outside environment).
3. Add perfluorocarbons to Mars' atmosphere, warming it up and also thickening the atmosphere slightly (by sublimating the frozen CO2 and releasing adsorbed CO2 from regolith).
4. Seed Mars with various genetically modified bacteria, which break down the toxic perchlorates in the soil, bind together the soil (to reduce the dust storms), digest nitrate minerals (adding nitrogen and oxygen to the atmosphere) and produce oxygen via photosynthesis. At the same time, robots could be used to begin building habitats for humans.
5. Add plants and animals, and begin human colonization.
6. Build an artificial magnetosphere for Mars, to help it retain its atmosphere (https://www.extremetech.com/extreme/245369-nasa-proposes-building-artificial-magnetic-field-restore-mars-atmosphere).

*: "semiterraforming" might be a better word for it

The most important problem is that today we can't even terraform the Sahara desert.¹ Thus, having an objective project plan is the far future yet.

Not only $rm CO_2$ has greenhouse effect. According this answer, the average temperature of an Earth without any athmosphere would be around $approx rm 0^circ rm C$. The current average temperature is $approx rm 15^circ rm C$. Most of the difference isn't caused by $rm CO_2$, but by water vapor and air.

The soil toxicity - large mass of perchlorate salts - seems probably solvable, probably with at least a little genetic engineering. There are highly sodium perchlorate tolerant bacteria. But there is no known organism which could survive and grow in the lack of water.

Although a lot of water was found on the Mars, this "a lot" is only compared to what we knew before the probes. The total known water mass of the Mars makes the whole planet still so dry, like a desert.

¹_{Although it would be technically possible, currently both money and politics avoids us to terraform the Sahara. An USA + China cooperation and some hundreds billions of $ could do it. I think the Martian SpaceX colony will happen first.}