On Towards the Stars: Building a Wonder
[This post is part of a larger strategy guide for Civilization 6]
The easiest way to build wonders is to click on the wonder, start building it, and wait till it's done. That's a great way to lose a ton of production from wonders getting sniped by other people. Any time you're building a Wonder, you should be doing the following steps, roughly in order:
Search the map to see if anyone else is building the wonder.
If someone else is already building the wonder, try and figure out roughly how many turns are left.
In 3D view, you can see what "stage" of construction the wonder is at; most wonders have 4-5 different in game models that they go through as the wonder nears completion.
You can roughly guess how many turns the wonder builder has left by looking at the population of the city, estimating the production per turn by looking at one of your comparable cities, and then dividing the total production required to build the wonder, offset by the current wonder stage.
If you want to get really technical, you can also try and see if your opponent has any woods they may be able to chop out and make a best/worst case guess at how long the wonder will take.
Look to see if someone recently picked up a Great Engineer that gives wonder production (or try and pick one up yourself).
Decide if you want to enter the wonder race. 9/10 times if someone else is already building the wonder, it's not worth it. But if you have builders, woods, Magnus, or just a ridiculously high production city, it may still be worthwhile.
Prepare to get the wonder. Generally you want to do some or all of the following:
Slot Magnus into the city building the wonder;
Build at least some builders to chop woods/rainforest and speed things along;
Move any trade routes to originate from that city and start domestic routes to increase production;
Slot in wonder production cards and governments.
You generally don't have to do all or even most of the above. It depends highly on how important the wonder is and how much visibility you have over what other people are doing. The less visibility you have, the more important it is to minimize the amount of time you are actually building the wonder, lest someone scoop you.
Obviously, actually build the wonder.
In rare cases, if you're about to lose a wonder race, you can declare war on whoever else is building the wonder and try and put your units on top of their wonder tile. This will stop your opponent from putting production towards the wonder until they can get rid of the unit.