Join a faction and get a castle and store a lot of cavalry inside it. Now go and attack and destroy enemy lords over and over. Always release them if you capture them. You will build up lots of honour and renown and exp from this. Try to get 150 or so honour. Now take more castles and ask for them from the king.
As for getting renown, I'm by no means an expert, but tournament wins is a good way. Fighting enemies that are stronger than you is another good way (early on, I can normally get decent renown for the Sea Raiders). Later, if you join a faction, joining battles against other lords is a good way.
To become a vassal about 200 renown is usually enough but it may take somewhat more or less depending on the circumstances. Female characters and characters that are not children of nobles may need more. If the ruler is desperate for help or likes you it may be easier. #7.
Joining a kingdom is one of the best ways to get renown in Mount & Blade II: Bannerlord. Once your clan level hits tier 1, you'll be able to enroll with a kingdom as a mercenary, so long as they
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