The job of a landlord is far from easy. When you rent out your property, you have to carefully vet your tenants and keep after them to pay their rent. You have to keep your property in good repair. You may even have to evict them if they don't adhere to the terms of your lease.
Late or non-payment of rent
Most landlords are aware that they can evict a tenant if they fail to pay rent. You may be able to do so if they're habitually late in making payments though as well.
If you plan to evict a tenant for making late payments or nonpayment, then you should send them a Notice to Quit. You should let them know that you're aware that they've been making late payments or that they haven't paid at all. You should let them know how much they owe. You may be unable to evict them if they start making timely payments or bring their account current after sending them this.
When you sent them this notice, you may find that they have a good reason for stopping payment of their rent. They may have withheld it because a safety or health violation persists. They may be willing to pay once the concern is remedied.
If a tenant remains in your property after the lease terms are up, then you can evict them.
You'll need to first review your contract to see if it's automatically set to default to a month-to-month tenancy after the lease ends. If it is, then you'll need to send them a Notice to Quit letting them know that you'd let them vacate your property within a set amount of days. If they don't, then you can commence eviction proceedings.
Other grounds for eviction
Most leases are written letting tenants know that they are to remain peaceful and quiet so that they don't distract others. They're also instructed to keep the property clean and free of damage. If your tenant violates the terms of the lease, then you may file a Notice to Quit advising them of their violations. You can initiate eviction proceedings a set amount of days after doing this.
Every state has a different requirement for how many days notice you have to give a tenant before initiating eviction proceedings. A real estate law attorney can let you know what the requirements are here in Utah.