The Sims 4

Well, in addition to what was provided by the other guide (using books), you can also cheat your way into grinding this skill.

So, to do that,you need to do the following :
Step 1 : Press , it should open a command box on the top left corner of your screen, press
Step 2 : Type the following into your command box Traits.equip_trait SteelBladder and then press Start to gain the trait SteelBladder.
Step 3 : Now repeat step 2 but instead of SteelBladder, enter the following traits :
Needs traits : NeverWeary (Energy need never decrease), ForeverFresh (Hygiene need never decrease), ForeverFull(Hunger need never decrease), NeedsNoOne (Social need never decrease). The only need that will keep going down, depending on the skill you're mastering is the "Fun" one.
Useful traits : Savant (Helps learn skills faster), MorningSim (Helps learn skills faster in the morning)/NightOwl (Helps learn skills faster during the night), sadly only one of those two can be picked.
{I believe I have listed all the traits I used to master my skills but if I forgot some, I will add them later.}

Once you are done adding all required traits, you can click on a microphone and select "Tell jokes" and then speed the game on the fastest one and let your Sim level up its comedy skill. Thanks to the traits, unless you have a job, you can go from 0 to 10 in one go.
Yes, its cheap, but since it doesn't disable your achievement, why not?

Hope it is useful! Please do leave your comments if you have anything to add.

To do this, you can either buy all 3 Comedy books (which'll rank you up to level 9) and/or buy a microphone ($250) and keep practicing on that. You could also tell jokes to other sims to improve this skill.
If you use the 3 books, you can only level up to level 9, so you will have to choose one of the other options too.