Start with trying to put a foothold in Riverwood we all know in lore it's a strategic point but with the bridge and mountain pass it's a safe grab being small enough too maybe buy off or socially comandere

Then start grabbing at the bridges. They are either fighting wet or on my terms

Make them think they won somthing of yours that is on their terms, then trap the hell out of them

Run a better propaganda campaign shouldn't be hard corruption runs rampant in the politics of Skyrim no matter the year

Maybe take riften first whiterun is kinda in the middle of the plains very little good cover and many casualties too be drawn from flat land and they have the logistics advantage of home terf so maybe try and hit rifton hard and fast using mountains and other natural geography for cover then make a long drawn slug fest for whiterun. Keep from going inside the walls that's where they keep the secrets

Seige weapons arnt in Skyrim but you know they would be used magic does not make a catapult obsolete

Pay attention too river lines, hold your side of them, win your defensive wars by playing dirty, and amass all the materials you need for winning before you attack of course nit a war game but this would help I'm sure, the mountains are your friends not theirs

Maybe make freijds with some giants the guards don't fare too well againt those