Some examples
When the referee is unsure on the awarding of a throw-in, the assistant

referee can indicate the direction by subtly pointing using a finger or

hand, held close to the chest. This technique is essential and very

effective in coordinating signals. When there are crucial decisions to be

made during play, or to indicate that the ball is in play, a discreet hand signal by the assistant might give valuable support to the referee. Using thumbs up or down gesture are signals of agreement with a decision or an incident as well as being a sign of cooperative teamwork and camaraderie among match officials.

Other signals
Subtle hand movements may be used to indicate that the assistant referee has seen an intentional hand ball, holding or pushing. Shaking a finger slightly from side to side may also signal that there was no foul. In general, assistant referees should not use their hands or arms to show players they are offside or are being given advantage. These signals are the prerogative of the referee and duplication by the assistant referees create confusion and problems. Shaking one’s head up and down is used to indicate agreement with a decision.

Signaling goals
To confirm that a goal has been scored, there is a conventional technique where the assistant referee runs a short distance up the touchline toward the halfway line to affirm a goal has in fact been scored. In cases of questionable goals to be disallowed:
The assistant referee stands in place while signaling the referee according to the situation as follows;
    If the scorer was offside at the moment the ball was passed to him/her, signals offside.
    If there was a foul by an attacker, stands at attention with the flag held straight down at the side
    If a player other than the scorer was in an offside position and in the opinion of the assistant
    referee was interfering with play or with an opponent, stands at attention with the flag held straight down at the side.
 

Assumes the proper position for the restart indicated by the referee.

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If communication devices are used
The assistant referee should use a minimum of words with this system because it is distracting to the referee and can lead to confusion. Examples would be "No" to indicate that a player is not in an offside position, and "yellow" to indicate agreement with a card. Care should be taken with this so as to not focus on what is said but on what is done.  Finally, to signal the end of the match, the assistant referee can use his fist, chest or hold up the flag to show the referee that it is time to blow the whistle to end the game. All these signals, while not official, in most cases deliver excellent results.