Starting your own kingdom goes more smoothly if you have a mid- to high-level character, high renown and Right-to-rule, mid- to high-level companions with as many points in Trainer as you can spare from their other skills, lots of fiefs stuffed with top-tier troops, the good will of as many lords from different factions as you can gather, and as many enterprises generating independent wealth as you can manage.
Having said that, sometimes it's more fun if things don't go too smoothly! It can definitely feel like more of an accomplishment if you can establish your kingdom while overcoming long odds, so feel free to pick and choose which of the above factors you want to emphasize and which you want to ignore.
To get more renown, fight a lot of battles, especially when outnumbered. Winning tournaments will also give you renown. Get married and throw a bunch of feasts: not only will your renown increase, but you'll increase your relation with your fellow vassals, which might come in handy down the road. If you have decent persuasion (or are not averse to reloading if you get a bad outcome), take on "Resolve Dispute" quests, which give a nice chunk of renown upon completion. You can get these by asking fellow vassals (or your spouse) if there's anything you can do to increase both your standings in the realm. These quests generally involve convincing two lords (or a lord and the liege) to reconcile, but if you take one lord's side, or fail to convince one or the other, you'll fail the quest. You may also, upon asking the same question to a fellow vassal, get a quest to denounce a lord to his face. Doing this will result in you dueling the lord, and if you win the duel, you'll also gain a small amount of renown (as well as a minor amount of controversy).
Increasing your CHA and Leadership stats will also increase the number of troops you can have in your party.