The Justice League was originally formed shortly after the modern heroes began to emerge. It was founded by the Martian Manhunter, Wonder Woman, Batman, Green Lantern, The Flash, Aquaman, and Superman. Initially the team was founded to deal with those threats that no hero could handle alone. Working to the idea that the heroes can get better results when they pool their strengths, it would for many of the members evolve into more than that as the roster changed and grew. The Justice League has saved the world many times over, containing a large number of different members and moving to several different headquarters. Currently, the League operates out of an orbital station with full U.N. backing, serving as the Earth's primary defense against threats of a planetary level as well as something of a social gathering point for many of the heroes of Earth.
The comms don't have a standard appearance thanks to everyone's very different costumes. That said, they all have the same inner workings.
They all allow for global communication with one another. Each has a holo display for information viewing, and seeing who you are speaking to. This can of course be turned off. (Missions don't often allow for bright, glowing things.)
Each has a tracing device. This can not be turned off unless someone rebuilds it. The tracing device serves a couple immediate purposes: Finding people when trouble hits, and the teleporter.
An emergency beacon. This must be activated for use, but it sends a signal to everyone that something is wrong.
Justice League Javelin-7s
As the Watchtower was improved, Batman created the Javelin-7 ships to replace the original Javelin shuttle. There are approximately a dozen in the hangar, and the primary use is still as short range travel and travel from Earth to the Watchtower, but can now also be used for long-term space travel and underwater travel. Each can hold upwards of a dozen people.
The Slideways transporter permits members to teleport to and from the Watchtower and the Earth for easy, speedy travel. Of course, the first couple times is not always the most pleasant experience.
Currently sponsored by the United Nations, this permits the Justice League more breathing room to work internationally. Of course, there are still limits by those not associated by the United Nations, or those that fight to keep their secrets.
Though Oracle is not currently an active member of the Justice League handling their operations anymore, she is still a resource for being called in to assist with their electronic security systems and more.
The Justice League not only has access to a massive database on supervillains, supervillain organizations, aliens, and research materials, but it is additionally supplemented now by filtered (for security reasons) data by the Avengers and in turn S.H.I.E.L.D.. This means they have even old information on the same from the other Earth before the merger. In exchange, they also share (filtered for security reasons as well) information with the Avengers and in turn S.H.I.E.L.D..