To start this off, let's have a little thought experiment here.
We still have the 20th century go on as usual... WW1 still happens in some form between 1914 and 1918, WW2 still happens between 1939 and 1945, the Soviet Union still existed between 1917 and 1991... but something's different about how history is playing out.
Maybe a surviving Napoleonic France is participating in WW1. Maybe in 1948 the devastation of WW2 brought about massive revolutions in Europe of varying colors following the war, and America goes to war with Mexico just as the troops start coming back from Europe and the Pacific. Maybe JFK or Nixon or whoever becomes president ITTL witnesses the beginning of a 2nd American Civil War in 1961, only to echo Lincoln by getting assassinated in 1965, assuming he still isn't assassinated in 1963 and it's his successor getting assassinated himself in 1965.
Not necessarily exactly like that, but this is to put things into perspective to get the thinking processes going. Simply put, it's taking events and nations from the 19th century and putting them through a 20th century lens, while keeping true to what happened in the 20th century. In layman's terms, you're mixing both centuries together, while at the same time balancing a 20th century authenticity with keeping things realistic. There's a reason I'm posting this in After 1900 instead of the ASB forum.
A couple steps to help out in trying to understand my thought process here. I'm aware I'm not the most intelligible person with conveying my thoughts, but please bear with me.
1. Go to Wikipedia and pick out some major events from the
19th century. Look into the articles on each decade too.
2. In your mind, replace all mentions of the year 18xx with 19xx (e.g. an equivalent to the Napoleonic Wars happening from 1903 to 1915)
3. If there are mentions of events from previous centuries, like the French Revolution of 1789 (or 1889 in this case) use these as PODs. Get rid of the constraints of a singular point of divergence and make up multiple points of divergence.
4. Compare each decade of the 20th century with its 19th century equivalent. What do the 1900s look like crossed with the 1800s? 1910s with 1810s? 1920s with 1820s? Rinse and repeat for each decade.
5. Ask yourself these questions: How would this event in the 19th century fit into the 20th century alongside what happened in the 20th century?
6. Keep some room for creativity. Not everything has to play out exactly as it did. Just go with whatever feels right, with more of a focus on how it would translate into the 20th century.
One final point... realistically speaking, what would the consequences be of an echo of each 19th century event happening in its equivalent years in the 20th century look like? What would the world look like in each decade?
What would the 1900s look like?
What would the 1910s look like?
What would the 1920s look like?
What would the 1930s look like?
What would the 1940s look like?
1950s?
1960s?
1970s?
1980s?
1990s?
2000 and beyond?
What would this altered 20th century look like?