Here are the required steps to locate Conan:

1. Accept Order for Sam [Order No. 37] Sewing Kit Delivery: Cosplayer. It can be found after Order 38 at a random terminal in Central Region. The quest is usually at "South Knot City" or "Distribution Center South of Lake Knot City". If it's not there, check the terminals at other facilities or sleep in private room. The starting location changes as time progresses.

2. Deliver the cargo to the Cosplayer.

3. Here you find Conan O'Brien! You meet Conan after talking to the Cosplayer. He tells you some jokes about Otters and hands you an Otter Hat!

4. You can equip Conan's Otter Hat from the inventory (press UP). When in water you have more control and can paddle quicker left and right and even do barrel rolls in the water.

And that's how you find the Conan O'Brien Easter Egg in Death Stranding. It's simply an optional order. You can still do this after the story if you forgot about it. The earliest opportunity to do this is at the end of Episode 3.