Going from car lease to own - help please!

I am thinking of going from leasing a car to buying when my lease is up in a month or so, but the dealerships are intimidating. I'm trying to figure all of this out before I walk in the door so that I feel more confident - I'd appreciate any advice!

The lease I have currently is valued at appx $13K (2015 Ford Escape, 32K miles) and I'm unsure of how this works when trading in the lease and the finances of it. I'm thinking of a Buick Encore or the like ($25K) and would like to buy instead of lease. How does this work as far as calculating the "trade-in" value of the Escape? I know that I don't want to give them a monthly payment amount and work from there but I'm unsure of how to approach them with this. Does the Escape even factor in to buying or would I likely still need to have a down payment after that?

I appreciate the help! I'm working out of debt and making better decisions - I feel like the car dealership is where I make some bad ones that follow me for years and I'd like to be better at this. Thanks so much!