After beating maliketh in farum azula, you'll automatically spawn at the capital of ash grace point which is perfect for reaching the colosseum. Start heading southeast and look for collapsed buildings near where those massive dragon corpses are lying around - the ash actually makes this part easier since you can climb over stuff that used to block the way. When you spot that golden spear stuck in some rubble (there's a nice somber ancient dragon smithing stone there by the way), you'll want to work your way west using the rooftops and walls, dropping down carefully onto platforms that lead toward the outer section.

The tricky part comes when navigating through all the dust and debris, but if you stick to following intact building structures westward, you'll find new paths that weren't available before everything got covered in ash. Just remember, timing is super important here - make absolutely sure you've grabbed the bolt of gransax before fighting maliketh if you're going for achievements, since that's one of those items that becomes permanently missable once the city transforms. Same goes for finishing up anything with goldmask or brother corhyn, since their questlines get cut off after the change.

Tip worth noting - even though everything looks different under all the ash, most of the basic layout stays similar enough that you can use the same landmarks you remember from exploring the regular capital, just need to be a bit more creative with the parkour now that certain areas have crumbled or opened up.