I’d suggest checking out the Impact Effects website
The main page will estimate various effects based on different impact parameters, and if you click “tell me more” at the bottom, you get a pdf that gives more info on the science involved, and describes more of what the effects would be like.
It depends a lot on how big an object you’re hitting earth with.
On the small scale, a bolide will explode in the atmosphere, so the main effect is the air blast. And that’ll be local. Still, if it explodes above a city… not good for the city. (This is probably what happened in Tunguska in 1908… fortunately, not a particularly populated spot.)
At a dinosaur-killer level, you’re looking at a fireball, which, if it reaches into forest, could spread across all touching forests. You get earthquakes too, though reducing in intensity when you get farther away. Ejecta is debris kicked up by the impact… you can get this landing pretty far away, and fairly close to the impact, that could be a rather thick layer, plus the biggest falling chunks would be like stony hail. Not fun to stand under. And there’s still an air blast… massive gales closer to the impact, triggering storms. Oh, and if it landed in the water, that’s triggering a tsunami. So you’re pretty much devastating a good portion of a continent, putting all that together. But the biggest cause of death would probably be a more long-term subtle effect… all this debris kicked up into the atmosphere is going to block out the sun for years upon years. And you’re going to have acid rain while the atmosphere slowly cleans itself. So, without sun, not only does stuff get cold, but plants die, and algae dies, which means not a lot to eat, and also oxygen levels are going down. The animals that survive the best tend to be small ones, ones that eat detritus and dead things… generalists, mostly.
If you’re talking about something ridiculously big… something bigger than has hit the earth since life got started… then, yeah, you can just melt the whole surface of the planet and vaporize the oceans. This would’ve happened a lot, soon after the Earth was formed, but fortunately it hasn’t happened since then