TL;DR: Normal conversation at 1 km depth would travel about 2 kilometers in water. The loudest scream a human could produce would travel about 3.14 km.
There are many factors that make it difficult to calculate how far sound travels, the biggest being pressure and temperature. The lower the temperature, the less far sound travels, the higher the pressure the farther it goes.
Calculation of the distance sound goes is difficult because not all the variables are known. But the principle behind sound losing volume over distance is called absorption. The sound also loses energy as it spreads out. The total energy loss of these two factors is called Transmission loss. Depending on the chemicals in the water, different amounts of sound are lost over different distances.
To do some math trying to get average values. The unit for sound energy is dB. Normal conversation has a power of 60 dB. In water, sound is stronger, so we add 62 to all values for sound in the unit dB. This means that normal conversation under water has the effective strength of about 122 dB. Normal voice frequency varies, but a typical frequency would be around 170 Hz. At about that frequency in most oceans, the absorption rate is about 0.06 dB/km. So we can see that the absorption rate is negligible (Though it will be included in the below calculations). But this does mean that frequencies have a small effect on the distance sound travels.
Now, sound also loses energy as it spreads out. Sounds spreads out in two different ways, spherically, and cylindrical. When the water is deep enough, it spreads out spherically, but when the water is more shallow, it spreads out cylindrically. This happens because the sound bounces off the surface of the water and the bottom of the ocean. So while some energy is lost when the sound bounces, more energy is lost when it travels out fully in a sphere. So sound travels approximately twice as far when using the cylinderical form. Sound spreads out in a cylinder when the sound does not fade before it reaches the top of the water (so it bounces off the surface) The amount by which the sounds distance dilutes over a given distance can be calculated. The formula for the loss here is TL = 20 Log(R). TL stands for Transmission Loss, and R stands for range/radius of the sphere. Because dB is logarithmic scale, we can directly transfer this into dB units. So at 1 km, this comes out to 60 dB, which perfectly matches the volume of human conversation.
So the total Transmission Loss is 60 dB/km + the absorption rate, which is 0.06 dB/km, which comes out to 60.06 dB/km
Generally, the threshold of human hearing is 0 dB. So using the data calculated above, the sound of normal human conversation (if it could somehow be communicated at the same strength underwater), would travel about 2.03 km.
Wikipedia says that the loudest recorded scream was 129 dB, which is 191 dB in water. So using the above calculations, at 1 km depth, a scream would travel about 3.18 km. Note, that is high enough volume to hurt human ears, so the underwater creatures should be able to handle louder volumes, or they should speak quieter.
There is one phenomenon that lets sound travel for much longer distances. This has been especially noticed from the noises whales make and it allows them to communicate over very large distances. When sound travels through water it slows down, causing it to refract downward. The water below keeps getting cooler, so the sound keeps slowing down and refracting. At a certain point, the water stops getting colder, but the pressure continues to increase. When pressure gets higher, sound speeds up. This causes the sound to refract upward. It then refracts back down as it gets back into areas where the water temperature slows. This refracting up and down allows the sound to travel a very long distance without losing much energy.
So there are a lot of factors that affect the distance sound travels, the biggest being pressure. At the standard pressure used by scientists the sound of normal human conversation would travel about 2km. But at certain depths, sound actually travels for a very long distance. This phenomenon is what allows whales to communicate over thousands of km. To a lesser extent it could work for human voices too, if not over crowded.
And finally I would like to say that this data is not fool-proof. There is no easy way to calculate exact values, so these values are not exact.
References and Notes:
There are some very good graphs showing absorption rates on this website. I got sound values and conversion rates from air dB to water dB from this site. Unfortunately, copyright prevents me from re-posting them here. For information on the full math I did to get the base TL for spreading out, see this site. Voice frequency information came from Wikipedia, as did scream information. Thanks to Irigi for pointing out some mistakes in my first drafts.