Actually, I'll just repost that answer here. Link-clicking is hard on the fingers...
That's a tough one to encapsulate. It depends. We mostly try to keep the spirit of the original, and the basic plot of each episode intact. So most of the situational humor stays (i.e. Shin is collecting stickers to get his Action Kaman/Action **bleep** belt). But most of the dialogue jokes from Japanese don't translate, either because they are Japanese puns or pop culture references.
Also, we are trying to appeal to a different group of viewers, so that means further changes to the jokes. In Japan this is aired during prime time and intended for all ages, and our dub is airing on Adult Swim. So, we try to alter the humor accordingly-- basically more jokes about poop, domestic violence, and eating homeless people.
Generally, we keep the storyline and throw out the dialogue itself. When writing a script, I read through the translation several times while watching the video, to get a handle on the plot and the conversations. After that, I put the translation away and write the dialogue fresh. Sometimes we end up staying fairly close to the original... And other times we stray pretty heavily.
Here's an example of where we stay fairly close to the translation in terms of content, and just change/add more jokes. This is from Episode 1, Shin's Allowance. Here's the original translation.
S=Shin G=Georgie (Kazama in Japanese) M=Maso
M: Say, how much is your allowance, Kazama-kun?
G: About 500 yen a month, I guess…
M: Wow, that’s a lot! I only get 100 yen a month…!
S: You could build a whole house...!
G: Get real! And pull your pants up!
M: Say, what about your allowance, Shin-chan?
S: I don’t have one…
G: Pull your pants up!
S: I get money from my mom when I want some.
But all she ever says is, “What’s it for?! Don’t you dare waste it!”
when she gives it to me…
G: Why don’t you have her set a monthly allowance, then?
S: Guess I will!
M: Yeah! It’s nice not having to ask for money all the time!
S: But she might not go for it.
G: Then why not go on strike?
S: A good pitcher’s throw?
G: Not that kind of strike!
S: So what do I do?
G: You refuse to help her until she gives you an allowance, for example.
S: I see…!
And our version (Joel wrote this one):
M: Hey Georgie, how much allowance are you getting these days?
G: A sweet 50 bills a week, plus stock options.
M: Wow. That's a lot. Are your parents doctors, lawyers, or Jews?
S: You could buy a whole monkey with that!
G: And you could buy a brain. Now pull up your **bleep** pants already.
M: So Shin, what kind of allowance are your folks giving you?
S: A whole lotta nothing.
G: Pants! Pull up your freaking pants!
S: Whenever I need money I have to ask my mom for it. But she never gives me any. She thinks everything I want to buy is dumb. What's wrong with Viagra, and Action **bleep** tighties?
G: You know how sad that makes you? You're an embarrassment to kids everywhere. She's playing you for a sucker!
S: (lands) Crowd goes wild!
M: Hey you know what? You should ask for a weekly allowance so you don't have to keep begging for money!
S: That'd be sweet, but what if she won't go for it?
G: Go on strike, like one of those lazy teamsters?
S: Throw a baseball at my mother?
G: Not that kind of strike, moron!
S: Okay, I'm confused.
G: Stop doing chores. That's what our Meximaid does whenever she wants a raise from my dad.
S: Oh, I get it!
And here's an example where we strayed pretty heavily from the translation. This is from episode 5, A Bootyful Day in the Neighborhood, where Shin meets a pervert on the street. As you'll see, in the original Japanese the man was not a pervert at all, just a man needing directions to someone's house.
Translation:
S=Shin M=Man
M: Little Boy.
S: Yeah, Mister?
M: I got a quick question for you…
S: You’re from Souka?
M: No, a place called Yashio right next to it.
S: Never heard of it.
M: Yashio has highways too, you know! No train stations, though.
Oh, anyways, do you know where I can find the Someya family?
S: Oh, the Someya-san that’s expecting to give birth to a wife this June?
M: Yes, the Someya-san whose wife is expecting to give birth this June.
S: This way! I’ll show you…!
M: Thanks, I appreciate it.
…
S: Someya-san! Someya-san! Souka rice crackers here!
S: Let’s see, I’m sure it was around here… Where was it, again?
M: It’s around here, right? I can look for it myself now…
S: Eh?! I’ll help you!
S: I’ll go ask a policeman, so hold on a minute!
M: No, you don’t need to go that far…!
And here's our version, thanks to the crazed mind of our other writing partner, Alex Muniz.
M: Hello, there.
S: What do you want?
M: Would you like to see inside this green bag? It’s full of cake and video games.
For the new GameStation Two?
S: Show me the cake, show me the game, show me the cake!
M: Sure, but first, you must answer me this one very important question.
S: Okay…
M: Would you prefer a Gigantic One-Eyed Monster with hair or without? I’m doing research on what kind of design little boys like you prefer, so if you could come back to my place for a few hours and tell me what you think that’d be super— there will be cake, of course, and surprises.
S: Oh… you’re one of those scums who wants to take my Action **bleep** Action Figure!
M: No, I just want to see how much you enjoy playing with my “Gigantic One-Eyed Monster!”
S: Sorry, but I can’t talk to strangers unless they have candy.
M: I feel like I can change your mind.
...
S: Help! Police! This scum won’t stop following me. He wants me to play with his one- eyed monster!
S: This is just like that very special episode of Action **bleep**. Attack of the Perverts.
M: Hey, little boy, cut that out! There really are video games in this green bag!
S: Really? And is there cake in there too?
S: Wait, that’s just another scum trick! I’m gonna get the police!
M: But you haven’t tested my new pink joystick!
Hope that sheds a little light on things.