Choose a city you want to invade, but instead siege a city next to it, wait until reinforcements arrive in that city then pillage every road tiles around it and then use some unit to cut reinforcement on the city you want to attack, preferably defensive units, and mobilize all your units to attack the city you chose to invade.

Actually, I just put my cavalry between city Metropolis, and city Junker. Then I move a stack of drafted riflemen next to city Junker.

Let the AI rush his defenders from city Metropolis into city Junker, and you waltz into the weaker one with cavalry and grab a bunch of wonders.

This is probably the stupid way to do it but much more entertaining. I just send big siege weapons and then hit everything else with a metaphorical BIG STICK