I am flying a similar route next month, although I'll be flying from Seoul (Korea) to London Heathrow (UK) with KLM. My first trip will be to Amsterdam (Netherlands) and then after about 90 minutes, I'll change aircraft and proceed to London.
If your flights were booked at the same time, the check-in agent should automatically check you onto your onward flight. If booked at different times, you'll need to mention your connection to them and hopefully they'll make arrangements for you.