A soapy taste in coffee is the mark of one of two things. Either:
(A) there is soap in your coffee! or....
(B) your coffee is underextracted.
Now the first suggestion that there may be soap in your coffee is not altogether tongue-in-cheek. There very may well be. If you think you taste something funky in your coffee, you should always check for foreign agents first: is the brewer fully cleaned, rinsed out and seasoned with coffee? What about your cup? When is the last time you took a look at the interior of your grinder hopper? (This may not seem like a likely source of soapy tastes in a coffee shop, but many home brewers keep grinders on countertops where they can get all kinds of other food or cleaning products in them.) So, first make sure the soapy taste isn't actually soap.
Because if it's not, you have a different problem entirely. One that's just about as common as a bar of Ivory soap. Soapy tastes in coffee are a mark of underextraction.
Remember: underextraction is not the same thing as weak flavor. A coffee can be full strength or even extra-strong and still be underextracted. And it could be overextracted and yet still weak (that's way too common for me to even think about right now without getting grumpy.)
Underextraction refers to what percentage of the solubles in the ground coffee are ending up in your brew. Each compound in a coffee bean — and there are hundreds — has a different flavor. Since the different compounds extract (that is, dissolve into the brew) at different rates, that means that a coffee extracted quickly will taste differently than one that takes a long time.
If I extract just 1% of a hundred coffee beans, I will have a full bean's worth of solubles, but they will be all the same boring flavor from that first moment of extraction. If I could somehow extract 100% of one coffee bean (not technically possible, but play along), I would have the same amount of solubles, but a much more overextracted, bitter taste. In fact, it would taste like chewing on a coffee bean. The fact that chewing on a bean is generally not as pleasant as drinking a well-extracted cup of coffee shows us just how important a proper rate of extraction is. If it weren't important, we would all just eat coffee instead of drink it.
There are devices that measure extraction, the most interesting of which is the Extract MoJo. I recommend at least learning about this topic if you are a professional. But the best tool — for professional and enthusiasts alike — is always your tongue. Remember Daniel's mantra: Coffee should taste GOOD!
The ideal rate of extraction is right around 20% of each bean. Keep in mind this has nothing to do with strength! Only flavor. If you want stronger coffee, you should just get 20% from more beans... not go for a higher percentage. If you want weaker coffee, back off of the amount of coffee, but leave it at a 20% extraction rate.
Practically speaking, getting back to soapy coffee, if your coffee tastes soapy, the water needs to spend more time with the coffee, or the water needs to be hotter, or both. If you run water through coarsely-ground coffee in under 1 minute, for example, you will have underextracted, soapy coffee. Pour the water more slowly, or make the grind finer so the water has to work more slowly through the slurry. There are also, of course, other factors (like water composition, and many others) that can affect extraction rate.
Some other words people associate with the taste of underextracted coffees are sour, minerally, metallic. To me, it sometimes tastes like a piece of aluminum. This is all on my mind because yesterday I poured myself a Chemex a little too eagerly and a Kenyan coffee that has been kind to me all week suddenly tasted flat, soapy, and just plain bad.
Remember kids, Don't Do What "Danny Don't" Does. Make your coffee right. Leave the soap in the soapdish, and the coffee in the pot.