The reading is a bit weird. It's kun'yomi readings across the board, meaning your knowledge of 建てる hopefully can come into play here. A building is something you build, so how do you say "to build"? It's 建てる (たてる). Since it's a thing you build, it's a たてもの. This reading is a bit confusing, but hopefully after a while you'll get it if you get it wrong too many times! Maybe if you think about the building you're in and call it a 建物 a few times it'll sink in better?
This is very nicely designed building, isn't it?
It's only been a year since it was built, but this building is pretty dirty already, isn't it?
"I’d like to go see the building with you so when would be convenient for you?" "Well, I’ll adjust my schedule accordingly."