As you will notice, there is an Ogigayatsu army in your province right at the start. Your capital is far away from this, so reinforcements from there won’t arrive in time. You can wait and build your army, but the Ogiyatsu will build just as quickly so you won’t gain any advantage. That means you’re best off attacking the army on turn 1, using both your field army and your Daimyo from the nearby town.
Since your Daimyo can fight night battles and gives +1 morale to all your troops, send him to join the army and move the other general away from it. Place him close to the enemy army, so an arrow indicating it can re-inforce in a battle against it appears. Then attack the army with your Daimyo and his men. This will make both your generals a commanding general, so they both earn experience. Winning the battle may be difficult, if you’re having trouble take a look at this replay.
After the battle, move the army to the border of the province, again placing the general close behind.
Recruit one Yari Ashigaru and one Bow Ashigaru to the field army. Construct Improved Irrigation in Sagami. Start research on The Way of Chi.
Send the new recruits to join the army. Build roads in Sagami.
You’ll get a missions to capture Musashi (the Ogigayatsu’s only province), so go ahead and besiege the town, again moving your second general close to act as reinforcements. Assault the castle and occupy it. Repair the castle, leave taxes on for now. Move the new recruits from Sagami towards Musashi. Start researching Todofuken. Upgrade the mines in your capital province, Izu.
The Bow Ashigaru will reach Musashi. Depending on how many men you’ve got left over from the battle, public order may still be below 0. If it is, exempt the province from taxes until it’s safe to start collecting them again. Build Improved Irrigation and Roads in Musashi and if possible a military building of your choice in Izu. Recruit a unit of your choice in Musashi.
From here you have two choices: continue expanding north-east or turn around and start expanding south-west towards Kyoto. On a short campaign I prefer going south, so I have around 20 provinces when I reach Kyoto, then I only need 5 more to win. On a long campaign or on Domination I prefer going further north, as there’s less to clans to get angry with you and the south is easier to defend.
Start by taking the provinces around Edo Bay, then go for Hitachi and Shimotsuke. Shimotsuke has a nice bottleneck on the northern border so you can defend there while expanding west into Kozuke and North Shinano.
The Takeda will most likely have emptied Kai to expand north, so you can swoop in and take their capital. This makes your north-western flank easier to defend and gives you access to horses to improve your cavalry. From there you can expand along the coast.