As long as both flights are on the same ticket, in this instance, this is what should happen:
- In BLR, when checking in, they should see both flights in your booking. They will usually reconfirm by asking “what is your final destination today?”.
- They will “check-through” your luggage to the final destination: you’ll see the labels they stick on your luggage will have both DEL (usually smaller print) and ORD (usually larger print).
- They will usually give you boarding passes for both flights
- You’ll go through security, to your gate, and board your aircraft.
- In DEL, you will not see your luggage, it will be transferred to the next flight.
- You’ll go through exit passport control and possibly another security check (don’t know the details in DEL)
- You’ll go to your gate and board your second flight
- In ORD, you’ll go through passport control (immigration), reclaim your bags, go through customs, and that’s it.
Make sure when you check-in that you are indeed checked through to your final destination.
If for some reason they can’t issue the boarding pass for the second flight in BLR, you’ll need to get it in DEL, usually from a “transfer desk”. The agents in BLR should be able to tell you exactly how and where.
In DEL, make sure you follow signs for “transfers” or “connecting flights”, not “exit” or “baggage claim”.
Depending on the airports and airlines there could be lots of staff around to assist you or none at all. But it is always quite well signposted.
Note that things could be quite different for other combinations of flights/airports (including in the way back).