There are a total of 5 jokes. Four of them are in chapter 5 (Pittsburgh) and one is in chapter 6 (The Suburbs). There is no progress tracker for the jokes. So make sure to get them in correct order. You can also do this via chapter select. For example: after listening to all jokes in chapter 5 you proceed to the next checkpoint (where some enemies spawn) and go back to the main menu where you load the suburbs area.
Always clean the shown areas of enemies and wait a minute until Ellie takes out her Joke Book. Sometimes you need to do a series of other actions to initiate a conversation with Ellie.
Here's how to make Ellie tell all her jokes:
#1 (0:05) - Pittsburgh "Alone and Forsaken"
Clear the area of enemies before climbing over the bus. Now wait in front of the bus until Ellie gets her Joke Book.
#2 (1:44) - Pittsburgh "Alone and Forsaken"
Kill all enemies in the bookstore and stand around for a while.
#3 (3:19) - Pittsburgh "Alone and Forsaken"
Turn around when reaching the flooded street. Look for a poster of a model behind a window. Look at it and talk to Ellie. Now keep waiting in this area until Ellie stops walking.
#4 (5:15) - Pittsburgh "Hotel Lobby"
After entering the Hotel you need to climb up a ladder. Get the artifact in this area and open the safe downstairs. Go back up the ladder and Ellie will start telling you more jokes.
#5 (7:05) - The Suburbs "Suburbs"
When reaching the suburbs, check out the broken house on the right. Wait in the kitchen and listen to the dialogue. Go to the other side of the street and look at the "I'm Armed" writing. Now go to the ice cream truck. Keep going down the street and check out the red symbol on a wall. Wait at this spot until Ellie tells her last few jokes.