Thee deeper you dig, the older the samples. Let me put it this way, during a Greenhouse Earth, temperatures around the poles dropped, allowing ice to form, right? Right now we can look back as far as 400,000 years ago, so let's go with that.

Let's say 400k years ago, ice and glaciers began to form, freezing the surface and partly beneath the water. So why do glaciers protrude from the water so high? That's because there's moisture in the atmosphere. Humidity. There's also rainfall that, when over colder areas, becomes snowfall.

Moisture lands on the ice and freezes, same with snow, maybe even rain in the earlier stages. I's like putting an ice cube in the freezer and adding a drop of water every day for a year, right? The ice cube will grow. Well that water contained or trapped air bubbles from that particular day or year. So as the layers of ice grow, the air bubbles from 400K years ago are buried deeper and deeper.

When it comes to dating the ice cores accurately (or as accurately as is currently possible), then it gets a little more complicated. Once again, it's kind of like counting rings in a tree trunk, but they compare other factors, like background radiation levels. Or they look over weather data from, say, 50 years ago and compare it to an ice core and see where the data matches at a certain depth. Then they use that ice core as a guide to help date other ice cores.

Quite honestly, it's a specialty field that requires a fair bit of knowledge. For example, I don't think many people understand how people measure the nutritional content of your food, right? It's not like they stick a vitamin detector in all the carrots. No, there's complex procedures for measuring these things, like removing all the moisture from a food sample or (and I'm serious here) blowing it up in a contained explosion.

That's not to say you aren't free to doubt and question climate change. In fact, I'd say read up on it as much as you can. Educate yourself on it so you can criticize or support it, but the biggest obstacle is not going in with you mind made up. Going in and automatically thinking "Climate change is real and everyone else is wrong" is the same as walking in thinking "It's a sham and everyone else is wrong." Climate change supporters and deniers have to both be open to the possibility that they could be wrong.