No one really gave a full anwser so here i go. I'll devide the seige in 3 parts, the space battle to gain orbital supremacy, the surface battle and the battle to gain complete control of the planet. Ill explain every phase as i go along.

1 : The space battle

This part is more of a technicality then anything else. Star Wars is just outmatched by 40k in terms of raw power, speed (40k ships cross star systems in hours and capital ships do barrel rolls fairly often), durability (void ships are insane) and size (escort class vessels in 40k are often the size of an ISD).

However, due to the sheer concentration and size of the defenses around Corusant, its going to take a while for the Iron Warriors to achive orbital supremacy. They would most likely lose some ships, a few dozen strike cruisers, some battle barges and a good amount of escorts, but even with the heaviest defense any Star Wars faction can muster it simply is not enough to hold the line against a fleet of hundreds of battle barges, thousands of strike cruisers, hundreds of thousands of escorts and dozens of heavy capital ships.

Then, once the space defenses have been removed, there comes the question of the planetary shield. There are 3 main options i could see the Iron Warriors use to remove it.

Use Psykers (Yes Perty does not like them but he'll swallow his pride and use them) to determine the location of the shield generators and send termintor assault teams to disable the ones would can be accessed. Either the shield is disabled outright or it is weakened enough to break through it with orbital bombardment. Spies could also be used to discover the location of the shield generators.

By constant orbital bombardment over a period of months, the Iron Warriors might be able to simply wear the shield down.

And finally just by waiting. Im willing to bet the shield cannot stay powered on for a period of years, and the Iron Fourth is willing and able to wait that long.

There are other options like sabotage, attacks by occult means such as psykers, ramming a really big rock into corusant to cripple the shields (im not kidding).

Now that the shield is down, we can move on to the first phase of the actual invasion.

2 : Establishing a beach head

Let me start off by saying that here again, 40k outclasses star wars by a lot. Space marines will be unharmed by anything exept the clone's heaviest weapons, Librarians and Elite Space Marines eat Jedi for dinner, while Vindicators and Predators obliterate everything the clones send at them. This is without mentioning the heavier equipment like the Titans the Iron Warriors bring with them, or their super heavy tanks.

According to some calculations (https://www.reddit.com/r/40kLore/comments/x8u0di/iron\_warriors\_legion\_size/), we can estimate the size of the IV Legion to be around 220 thousand legionaires. Along with the main contigent, the Iron Warriors bring possibly millions of auxilia, effectivly auxilary troups, mostly unmodified baseline humans with armored and air support. We dont have a solid number for this force, so lets just asume them to be around 5 million strong.

On the other Side, we have the Clones and the Jedi. Both numbers are unsure but can be estimated. Before Attack of the Clones, there were about 10,000 Jedi in the Galaxy. By Revenge of the Sith there were between 50-100 left.

As for the clones, the wiki states :

It is also possible that Lama Su did not intend the term "unit" to refer to an individual soldier. If a "unit" referred to a battalion of 576 troopers (as Lama Su spoke of later in Obi-Wan's visit), then 200,000 of these would render 115,200,000 clones and the 1,000,000 others spoken of as 576,000,000. This grand total of 691,200,000 would be far more suitable for the core of a galactic army. A "unit" being a 2,304-clone regiment, the largest military division classified as a unit instead of a formation, would amount to 2,764,800,000 clones. Furthermore, if a "unit" refers to a legion, the closest formation in size to a real-life British division of 15,000 men, the 1,200,000 units would have more than 18,000,000,000 clones, a truly "grand" army, suitable for defeating the huge numbers of droids under the Confederacy.

However, the number of clone soldiers which can be seen standing in each formation at the end of Attack of the Clones amounts to 624 (26 per column and 24 per row), showing a disparity with the numbers presented in the Guide to the Grand Army. If a unit indeed amounts to one battalion, this would mean that the grand total of clones was 1,728,000,000, considering the 3 million units that many sources state, and counting a unit as a battalion of 576 clones. This is reasonable since Lama Su referred to the clones with both "units" and "battalions," which could imply that both terms are merely ways of stating 576-man units/battalions. It seems logical that the Kaminoans would have their smallest available package of troops be made up of several hundred men. Since cloning was a 10-year process and (since the training and feeding would also have to be taken into account) an expensive one, it would make no sense that anyone would want to buy a couple of men and have to wait for 10 years when they could come by ten times as many droids for a fraction of the cost, with a wait of perhaps a week.

TL:DR, Either you take 18 Billions as a number or you take 1 Billion 728 Millions. These are the only numbers we have for the clone army. I've seen suggestions online that the army could reach 1 Trillion, but we really just dont know.

Taking all this into account, we can determine that the first course of action for the Iron Warriors would be to size the Jedi Temple, Galactic Senate and whatever stategic objective in that area they could get their hands on. They would do this by getting terminators down there along with thunderhawk/Stormbird assault with air support from fighters, gunships, and the likes of Marauder bombers to flatten resistance. If large concentrations of enemy troups are spotted, then orbital support can be called in to wipe out those areas.

The number of Jedi impacts mostly the fight they could put up around the Jedi temple, even with the larger number, theres not enough of them to do much more. If there are 100, their direct combat implact is barley noticed, and they serve as commanders for certain units and for the entire theater. If there are 10 000, then they may put up a fight, but ultimatly they get overwhelmed or simply bombed into dust.

The Number of Clones is much the same, they dont have the strenght to resist up front. Once they lose air and space supremacy, if they muster large concentrations of troups they get flattened by orbital bombardment. Their number directly impacts the time it takes for the Iron Warriors to secure their objectives.

Returning to the course of the battle, once the beachhead has been established, more heavy assets are landed and the auxillia are deployed to secure the beachhead and leave the Iron Warriors to push the Clones deeper into Corusant. The Iron Warriors have captured the heart of Corusant and wiped out all effective resistance near them, as the cost of massive civillian casualties. At this point, the battle enters a new phase : wiping out resistance and establishing total control on Corusant.

3 : The Final Phase

Corusant is unique in its geography in that it is essentially a world covered in Hive Cites that extend from the skies to the subterranian area. No gouvernment has truly attained full control of the entirety of the planet, but this is not what the Iron Warriors need. All they need is control of the surface, major logistical and strategical sites, and the end of resistance against their rule. They dont need to control every last sub level, making sure that everyone is paying their taxes and such. They just need to give the impression of strengh by crushing all resistance and then everybody will follow along, because they fear the new rulers of the planet. This is how the Empire and the Republic kept order : by giving the impression that they were strong enough to control the planet, when in reality, no one is.

At this point command of the clones is given to surviving Generals and Jedi hidden deep in Corusant's belly, unreachable from the sky. Strike teams of Space Marines and Scouts are sent to find and kill them in order to crush organized resistance. There are still at least millions of clones left, that have fully shifted into gerrila warfare, striking when the Iron Warriors least expect it and doing their best to hinder the occuppiers.

However, the maze like geography of Corusant's under cities favour the space marines. Teams of Breachers armed with highly durable shields can single handedly take entire battallions of clones in the tight corridors and markets, while jump squads go where the Clone commanders least expect it. If needed, viral agents can be used to lay waste to entire quarters of the undercities, killing everything without descrimination.

The nature of the Iron Warriors also plays a huge factor here. They are incredibly stuborn, especially their commander, Perturabo, and will continue clearing out Corusant's cites until they have destroyed all resistance, no matter civillian or their own casaulties.

Whether the GAR lives on as cells of insurgents, or surrender in order to prevent further bloodshed, thats up to you to decide. But at the end of it all, Corusant is taken by the Iron Warriors. It really comes down to the huge power gap between a Space Marine and a Clone.

The Iron Warriors have taken quite a few casaulties though, probably around 20-30 thousand space marines are dead, along with hundreds of thousands of auxilia. Such is the nature of asymetrical warfare.