There is a lot to know about this game, it took me two months before I had any sense of what I was doing. Hopefully this guide will make it a bit easier for new players!
Ask for barters in Alliance Chat! We're a friendly bunch and can always send a few SS your way to help you earn more silver!
Your early silver should be focused on upgrading your Counting House and Village Centre. The Counting House upgrades will pay for themselves and more after a time, and being able to produce your own resources early on is a big help.
Pick one of the three main stats (Battle, Trade, Intrigue) and focus on it. Multi-classing is viable later on, but if you spend all of your early silver upgrading every building at the start you'll run yourself dry very quickly. Each Fealty has their own preferred stat, so sticking to the stat of your fealty is a good start. Starks, Baratheons, and Greyjoys should choose Battle; Lannisters, Tullys, and Tyrells should choose Trade; and Targaryens and Martells should choose Intrigue. Don't worry, after you've played for a while you'll have oodles of silver to spend!
Your character strength adds to the strength of your Sworn Swords (SS). The stats on your character, in the upper left, are added to all of your SS's strength. Therefore, equip your best gear on your character--even modifiers like +% attack or +% barter will apply to all of your SS.
Your building strength adds to your character strength. And since character strength adds to your SS strength, upgrading buildings will make every one of your SS stronger. Not gonna lie, it took me two weeks before I figured this one out... yeah.
You can skip the last 5 minutes of just about anything for free. When the completion timer is under 5 minutes, cilck "View Progress" on the construction/quest/production. The first option will let you skip the last 5 minutes.
Acquire several cheap (common) SS when you have the silver to spare. This will let you complete multiple quests at once, or send some out to complete adventures for extra resources and silver. The more expensive SS aren't worth the silver quite yet.
Train the SS you have. SS gain XP through Adventures (mainly) and can level up their stats. Until you hit 200 in your character's main stat, it can be a good idea to stick to leveling the SS's main stat (Battle, Trade, Intrigue) over its specialty (i.e. Barter, Harass, Steal).
Learn the quest icons. Quests with the castle icon don't require a SS to complete; for these quests, all you have to do is select an option and you'll earn some silver and a resource. Quests requiring a SS will have the icon of a helmet and two red banners.
Don't wait on bonus objectives to advance to the next chapter of the story. You can flip back through the quest book and collect them later when you finish them!
Try to log in at least once a day to collect your daily rewards. This will allow you to collect your Daily Quartermaster Key to give you a chance at peerless gear and seals. You'll also earn Daily Rewards, with ~600 silver every 4th day, which is a nice bonus early on, and Gold every 7th day, which you can never have too much of! Your Daily Reward progress will reset to 1 if you miss a day, so try not to let that happen.