Hey! There are 2 changes from First Edition to International rules, so:
1. 2 points for two-tile cities -> 4 points for two-tile cities:
Value them more in every way. In most scenarios, if you draw a city cap and there's an empty city cap available, take it. If you can avoid leaving an empty city cap, avoid it, or if leaving one open is what you have to do, make it complicated (point it towards a road or field or a big-and-hard-to-complete city). If you draw a city cap and there are no empty city caps available, try to meeple it in an out-of-reach kind of way (e.g. pointing outwards with no immediate invasion/harrassing opportunities). And always remember there are 23 city caps in the game, so if you draw the last one, no point in trying to meeple it for 4 points! Try and do something else with it.
2. Field changes:
Think of the field as a feature of its own. When you are building a city or road, opponents can invade them. If there's a meeple tie, you share the points. If there's a majority, that player takes all the points. It's the same with the fields. Each field is its own, and each field is adjacent to a specific number of cities that count for its points. As usual, the limits of the field are roads, cities, and the river, and there can be a tie or majority for
each field. However, the main big change with this, is that sometimes there is a cluster of small cities that are adjacent to 2 fields at the same time! Imagine you have a big field that, in one side, has 3 empty city caps right next to each other. When closing those city caps, the tiles that are closing them are forming a new field right next to the big one, but that isn't connected. Before, this would simply mean you have one more meeple adjacent to these cities and, therefore, have a bigger chance on having a majority for them. Now, you have 2 separate fields scoring independently those 3 two-tile cities, scoring 18 points for them, instead of the usual 9. Maybe it's hard to picture it without an example in-game, so I'm sorry if it wasn't that clear. To sum up the field part, before, you scored EACH CITY. Now, you score EACH FIELD.
Hope this was kinda helpful! GL and HF