In the past, I have given the tenant the benefit of a doubt and allowed them some time to get current. I generally do not allow it to go past two to three weeks, but again, I am willing to work with them if they communicate and it's cordial. That being said, you're past that point.
Remember - sending the letter, filing, even getting a judgment doesn't obligate you to evict the tenant, and they can get current at any time by paying what they owe. Keep VERY good track of EVERY expense - postage, envelopes, mileage to and from post office and court, etc. I can send you a tracking spreadsheet I developed to help me make sure I am keeping all costs in front of me.
For the notice, make a copy of the form you send, take it to the post office, and get a Certificate of Mailing. It costs $1.35 or something and shows you mailed the letter. Sign the second page and keep the receipts, etc. send a 7 day notice for late rent, 30 day notice for lease issues.
I just talked to the local court here, the 34th District Court in Romulus. (You should call your court as the practices are sometimes different.) They said the notice is considered delivered the day it is mailed, but you have to give at least 8 FULL days before filing for a judgment. So, if you mail tomorrow (the 11th), you could file for judgment on the 19th. (7 days to the 18th, plus one day to allow for 7 FULL days.) Typically the court allows some set amount of time to notify the tenant. In Romulus, it's two weeks minimum and Landlord Tenant cases are on Thursday. So, if you file on Thursday, the court date is typically in two weeks. If you file on Friday, it's two weeks and six days. You'll need envelopes, stamps, and multiple copies of the lease to attach to the complaint, and you'll probably want to pay the court officer to serve the papers. (I've been told you cannot do it yourself.) Get the forms at the court - they usually cost a dollar or two but they will be correct and have copies attached. Then you wait until the court date.
Go to the court on the date. If the tenant doesn't show up, you basically fill out the paperwork and get a default judgment. If they do show up, you can try to work something out with them or go in and see the judge. IMPORTANT - if your rental is in an LLC, you cannot talk to the judge yourself, and you must have an attorney. I think it has to do with the LLC being its own entity and you not able to represent the entity (unless you're a lawyer). I've gone four times and never had the tenant show up, so I've never had to go before the judge.
You can do all of this stuff yourself. I have used an attorney so I could see the process one time, and then I just used the forms filed as a template and did it myself. Lawyers in my area generally handle evictions, beginning to end, for about $250 plus filing fees, assuming it doesn't get complicated. That decision is yours.
Once you have a judgment, you have to wait 10 days that the tenant gets to pay the rent. They have to pay you everything due, not just part of the rent, but if you accept partial payment it could reset some things. (There are check boxes for this on the forms.) After the 10 days, you can file for eviction. I have never gotten to this point - the tenant has always paid or moved out by this point. Can't give you any advice on going forward.
Obviously, I'm not a lawyer, but this is the general process. Like I said, if you have the time, can get to court, etc., you can probably do it yourself. Google "eviction michigan" and there are lots of references. If you don't want to do it yourself or can't there are plenty of lawyers around, and their advice would obviously be more valuable than mine. I'd suggest getting a lawyer close to the court that you use as it minimizes travel time and costs that the lawyer might charge you. Hopefully the tenant leaves without you having to go to actually hauling out their stuff.
If I missed something here or you have a question let me know and I can try to answer it.
