I played my first game as Satake, who start with 7 provinces. It was a learning game so I played on normal difficulty but I had no problems in winning at all. I began by attacking and taking over my smaller neighbouring clans to the north up to the northern peninsula, leaving only a couple of small neighbours as a buffer between myself and uesugi, who were the largest clan, until I was ready to attack. I then ensured the remaining local small clans were all friendly to me, conscripted them to a plot and invaded uesugi, who were also at war with another large clan (I think it was Hosokawa), and so were crushed between the two of us and their provinces divided. I then attacked the neighbouring small clans one by one, grew to a size to rival Hosokawa, then attacked and defeated them. In the end I vassalised them, took all their remaining provices, and now owned 60%. The only remaining clan, Ouchi, did nothing to oppose my claim to the Shogunate.
Not once did another clan declare war on me.
Now playing as Kono on the highest difficulty, have secured my island position by defeating Hosokawa, and am increasing my power by slowly eating up my small neighbours. I'm trying to get my largest vassal to rebel, just to make it more interesting, but he won't bite just yet.
Over all I would say keeping this in mind will give you victory - be sure you know your aims in war, be sure they are achievable, and be sure to achieve them. But then that's the same for any game.