Let's focus entirely on communication with Mars. This is the target planet for most manned missions and the Moon is able to communicate directly with Earth without special systems.
In order to communicate effectively with Mars there are a couple issues that must be overcome. One is the six minute time-lag caused by the distance to Mars. The other is the fact that signals are periodically blocked by wither the planets or the sun moving in front of the communication satellites.
The second problem is the simplest to solve. It just requires more satellites. Perhaps two around each planet so that the signal is never hidden when the satellite goes behind the body. At least two would have to be built around the sun for the same reason. Mars One is utilizing a system like this for its communication with the colony it intends to establish. But they will only be using three satellites. One around each planet and then the sun. This system will ensure that there is only a few two hours periods of blackout when a planet is in the way as well as two week periods when the sun gets in the way.
While the system is effective, for a limited mission, it is not ideal as the colony grows and activity increases. Two weeks of blackout will not be acceptable. A problem of bandwidth will also arise, with increases traffic, which will require multiple satellites in order to transfer information quickly and reliably enough.
Eventually an network of dozens of satellites around the sun and each planet will have to be created to ensure optimized 24/7/365 communication between the bodies.
Then comes the issue of time lag between planets. Relativity stops us from overcoming this problem with available technology. There is no way to have a live conversation effectively between Earth and Mars. So ways of creating the illusion of instant connectivity will have to be created.
Again using Mars One as an example. They intend to allow astronauts to download websites to a colony server to browse on a regular basis. All this requires is a periodic data-dump to the colony with a copy of your Facebook feed from 4 hours before.
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Now this is an audacious goal, one which would take perhaps decades to implement but it can begin now. A space communications company can be created which could initially be profitable be serving as the communications hub for NASA research missions as well as potential manned missions. If someone moved quickly enough they could be contracted by Mars One to build and launch a system in the next five years.
It might not even be necessary to build everything from scratch and launch it. If the budget is really tight, it might be possible for a company to purchase existing Mars satellites that are considered obsolete, then refurbish them remotely to become an effective communications network, limited though ti may be.
Such a communication entity would ensure that systems are standardized for all missions since agencies and companies will not want to develop their own communications systems when they can simply piggy-back an existing one.
The business model for a space communications company would most likely be one of a basic data plan. How many gigabits does the organization want to send across the network? OK. They cost this much. This has worked well terrestrially and there is not reason to think that it wouldn't in space.
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Companies such as SpaceX obviously realize this potential. SpaceX recently announced partnering with Google and Fidelity to create a space-based internet service for Earth. This is just a stepping stone, to pay the bills, until Musk can create the connection with Mars.