Get them to confirm in writing what your monthly payment is, what it includes, and what the total amount due at signing is. They’re not going to tank a guaranteed sale and risk a negative reputation over something like that.
If you already know you like the car (have driven that model before), you could request they overnight you the paperwork so you can see it and sign it before going there.
Well you can start by researching reviews of the dealership in the internet. Then you can politely ask them to send you a term sheet with msrp, sales, down and monthly. That still offers no guarantee since bait and switch also happens in the dreaded finance dept after all terms have been agreed to and documented. Be ready to walk away then but let them know that you are ready to buy immediately on the original terms.