To begin, simply follow Joel's lead until you reach an area with a large dinosaur statue, interact with the nameplate to add an entry to your journal, then climb to the top of the dinosaur and dive into the water.
Finally, follow Joel a little further to find yourself in a museum.
Explore the Museum
Once you're inside, grab the hat from the right and then go into the exhibition hall ahead. Here you'll want to grab the Trading Card from the bench to the right, now put the hat on two dinosaur heads, then put it on Joel's head for a Trophy.
Looks Good On You
Put a hat on your companion
Note: During your look around the exhibition hall you can interact with each display to get some information on each dinosaur.
After you're done exploring the bottom floor, head up to the second floor and interact with the bench in front of the display of rockets to add an entry to your journal, now grab a helmet from the left and jump into the Space Shuttle for a cutscene.
Once you've exited the space shuttle, wait for Joel to open the door ahead, then dive into the water, now use Joel to climb into the building and then look for a way to open the door. Go into the open room and collect the Trading Card from under the bench, now follow the path along until you crawl through a hole and you'll find an Artefact by a body.