Answers: There is no standard form. The written words " I will not be renewing the lease" is sufficient.
No explanation is needed.
Why do you want them out? Tell them the new lease will bring to the fore the rent by $100. They'll take the connotation (or you'll get plentifully more rent).
Simply tell them you will not be re-newing the lease. You of late give them a 30 Days Notice to Vacate one month beforehand the lease ends.