Communication over radio seems easy enough until there is a lot of information that needs to be relayed. Chaotic comms can lead to misunderstandings and as a result poorer efficiency on the battlefield. For that reason a few ground rules of radio communication help to keep it clear.

The most important rule is to only say the important thing and to do it smoothly, quickly and in a way that everyone can understand you (clearly). It helps to take some time before sending a message to organize what you want to say in your mind. 
To avoid talking over each other it is important to mark when our message is over and what kind of response or lack thereof we expect.

So when our message is over but we expect an answer from the receiver we end our message with over.

When our message is over but we don’t expect or don’t need a response, we simply end the message with out.

Additionally, if we want the receiver to give us some time to respond we simply respond to their question with standby.

If we have to stop the transmission but our message isn’t over, we simply end the transmission with break. And then continue after a short period of time. This call can also be used to clearly change the receiver of the communication. Additionally if we have something very important to say and want to make sure the radio chatter stops, we simply start our message with break, break, break and everyone knows to stop talking and listen to the message.

The radio discipline described is obviously for the purpose of mil-sim gaming whereas IRL it might sound similar, it is often way more structured.

Examples of radio communication:

Alpha to HQ, over
Alpha this is HQ, transmit, over
HQ, Alpha requests medical supplies to grid coordinates 1 8 5 break 0 5 6 numpad 3, how copy over
Alpha, HQ, good copy, medical supplies to grid coordinates 1 8 5 break 0 5 6 numpad 3, over
Alpha confirms, over
Alpha, in 5 mikes supplies will be delivered by helo, mark LZ with green smoke, over
Alpha copies, supplies in 5 mikes, marking LZ with yellow smoke, Alpha out

In this example Alpha asked HQ to organize a supply run for them. They gave their location, HQ confirmed it to make sure they heard right and told Alpha to mark an LZ which Alpha also confirmed.

Anvil actual to Anvil 1-1, come in 1-1
Actual this is 1-1, over
1-1 we’ve got reports of movement around the buildings 100 meters west of your position, break…
…
move to the north-west to overwatch that area, how copy
Actual, 1-1, good copy, moving north-west to overwatch the buildings west, over
Break, break, break, Anvil 1-5 to all anvils, contact, bearing 120, distance 500 meters, two T-72s in the open moving left to right, Anvil 1-5 engaging, out
This is Anvil Actual, good copy 1-5, break, all anvils reposition to engage targets, bearing 120, distance 500 meters, out
Anvil 1-3, two times T-72 destroyed, bearing 130, 1-5 confirm targets destroyed
This is 1-5, affirm, targets destroyed, good shooting 1-3, out

The acting commander of the unit with codename Anvil was telling one of the sub-units to check out a contact report, but before the communications could be finished, Anvil 1-5 noticed two targets that could threaten friendly forces. Realizing that was the priority target, they stopped other comms and reported the contact using the 3D method. 1-3 was able to destroy the T-72s and double checked with 1-5 to make sure it was the same target and 1-5 responded with a pat on the back.

Radio Checks

When connecting to a new frequency or starting a mission it is important to check if our radio is working properly. Sometimes the squad leader or some other entity will request a radio check but even if they don't it's worth doing it anyways. Additionally whenever radio comms are not clear or someone is not responding to our call outs it might help to send a radio check and make sure we are indeed being ignored rather than our radio is not working.

Radio checks are performed in a number of different ways, but it is important, just like with any other communications over net, to be quick and precise. That's why most use a simple procedure for radio checks.
It will start with the person checking their radio saying providing their callsign and frequency they are checking and relay that it is a radio check.
The recipient, being anyone on the net will respond with something along the lines of: Good check or my personal favorite: check five out of five.
The second message can relay much more information to the person checking the radio. It tells them the connection is as strong as it can be or if the response is for example: two out of five, it is obvious that the signal is disrupted but still somewhat readable.

Example:

Bravo 2 radio check on 50, over
Bravo 2, Bravo 3, five out of five.

This of course are simplified prowords. We can also use terminology such as:

• Loud - very strong signal
• Good - good signal
• Weak - weak signal
• Very weak - very weak signal
• Fading - At times signal cuts out

and

• Clear - excellent quality
• Readable - satisfactory quality
• Unreadable - quality so bad that the message can't be understood

Usually you would combine one word from the first list with one from the second to create a message relaying all information needed for a radio check.

Radio use in Arma 3

For the guide on using TFAR in Arma check out this post.