If you have recently purchased and installed Don't Starve: Hamlet on Steam, your game's main menu screen colour would have been changed to green with the game logo changing to reflect that Hamlet has been added.
If not, close out of the game, and on your Steam library right-click on Don't Starve > choose "Properties". In the Properties window, click on the "DLC" tab; there you should see if Hamlet has been added and installed. If Hamlet has a check mark on "INSTALL" that means the DLC has been installed and added to the base game.
If Hamlet does not have a check mark, click on "INSTALL" for the DLC and close the window. Then click on "LOCAL FILES" in Properties and verify the integrity of game files – this will ensure that the files Hamlet is downloaded and installed completely.
Once in game, if you would like to play the Hamlet content, in the main menu, click on Play > New Game > check "HAM" to enable the content. Click on Start to generate a shipwrecked world.
Should the issue persist, your best, next step is to contact Steam Support and inform them of your purchase and installation issue. Steam Support will be able to check your account and provide assistance promptly.