General meaning:
* Settle: This is the most common and direct verb. It can mean to make a place your home, to resolve a dispute, or to calm down.
* Establish: This implies setting something up permanently or firmly.
* Resolve: This emphasizes the act of finding a solution to a problem or disagreement.
* Determine: This implies making a firm decision.
Specific contexts:
* To settle a bill: Pay or discharge
* To settle a dispute: Resolve or mediate
* To settle down: Relax, calm down, or rest
* To settle in: Become established, acclimate, or adapt
The best verb to use depends on the specific situation and the nuance you want to convey.