This was one of the instructables Burning Questions, and since we had recently been through correcting several bad behaviors of Murphy's (our little Jack Rat) I thought I might have some helpful tips - I am not a dog trainer by any means - Murphy is the first dog that I have had in 30 years and what follows is what worked for us.
Step 1: The Set Up - Bribery
I think the dog should first know a few key words and have clear associations with them. The best first word? How about "Cookie"? It will make everything else easier and funner for your pup to learn.
As with all lessons you wish to help your dog with, repetition and consistency are key. With Murph it took about half an hour to get the basic idea of "cookie". We really let her pig out the first day. We'd hold the cookie where she could see, say "Cookie?", and immediately give her a small piece of the cookie. Then repeat. Repeat again. ...and again. After we were sure that she had the sound of the word associated with the delicious treat we would begin giving them to her at random, but always say the word and immediately follow up with the reward. After a day she was a junkie. She will now do anything for a cookie, and since she knows where they are kept she will run to them any time she hears the word.
If your dog doesn't like cookies, use whatever they show a serious preference for. If you have a good relationship they will let you know what works for them! Just be sure to heap the praise on them whenever they get their special treat - it make it all the more rewarding for them and they will associate praise with the treat.
Step 2: The Pay Off
Once your dog has demonstrated a preference for a reward you can add words to their vocabulary. In the case of this instructable "Down" is a good choice. "Sit" is similar, and would be taught in an almost identical manner. The difference between "Down" and "Sit", in my (and Murph's) mind: "Down" is my reaction to a bad behavior while "Sit" is a 'trick' she gets to perform to get a cookie.
When we eat at the table or I sit in a chair and work on the laptop Murph developed a terrible habit of jumping on your lap and/or begging for attention by jumping all over you. This was also a nuisance for any and all house guests because poor Murph would just go insane with joy all over them.
I will admit that it was next to impossible to get her to listen when she was stark raving mad. Not even the promise of a cookie could calm her. So I had to get her to learn "Down" outside of those circumstances. When she was calm and would get on the couch I would say "Murph - down" and put her down on the floor. Then give her a small piece of dog cookie. At first she would eat the cookie and jump right back on the couch. So again "No, down" in a nice friendly voice and lift her back to the floor and a piece of cookie. Then if she would act like she was going to jump up I would put my hand on her haunches with only enough pressure to prevent her from jumping up while repeating "Down, Murphy. Good girl!" After she showed some inclination toward understanding we would delay the cookie a bit. It was not long (a day or so) before if she were on the couch and I said "Down" she would get down - no cookie required. Again, repetition is most important. The more times in a row the quicker she gets it.
This meant that we were ready to associate "Down" to the other circumstances and not just the couch. Every time she jumped on us we would say "Down" - she already new the word, sometimes we would have to get firm and say it 3 or 4 times, but she would get down. The heap the praise and get a cookie!