Tenant is likely breaking lease - Process to prove and evict

[Mike Fuchs]

Hi, new landlords here. We just bought a duplex and moved in two new tenants on Jan 1st. I feel we were very diligent/clear with our screening and rules, so now we need to act on what we said in the application process.

Received a call from one tenant today, she definitely had been holding back from calling sooner. One, the other tenant has used up all of the available garbage resources both weeks and then some. During a move, I get it, but she went on to say she is pretty certain at least two adults are living in the unit that are not on the lease (a clear violation of our lease). Additionally, one of them is smoking on the property, another lease violation. I walked the property today and found several cigarette butts. 

I don't want to micro manage the property, but as I was about to leave, I took a phone call in my car and watched two other people enter the property who are not on the lease, thus confirming the tenant's concern in my opinion. 

Both of these violations make this a tenant we want to remove. What is the best way to start this? We have occupancy rules in the lease, along with a clear no smoking policy for tenants and guests. We need to be sure to follow the rules, so anyone have ways they have proven these violations?