1. Give Tasleem:
The Messenger of Allah (PBUH) was asked:
'Which Islam is good (in terms of action)?' He said: 'To feed the people and to say Salaam to those you know and those you do not know.'
2. Lengthen the greeting:
A man entered upon the messenger of Allah (PBUH) and said:
The Messenger (PBUH) replied to the Salaam. Then the man sat down and the Messenger (PBUH) said: 'Ten'. Then another man came and said:
'As-salaamu alaykum wa rahmatullah.'
The Messenger (PBUH) replied. Then the man sat down and the Messenger (PBUH) said: 'Twenty'. Then, another man came and said:
'As-salaamu alaykum wa rahmatullaahi wa barakaatuh.'
The Messenger (PBUH) replies. Then the man sat down and the Messengeer (PBUH) said: 'Thirty'.
Look at how much loss of reward a person inflicts on himself by sufficing himself with only a part of the salutation. The person should say the entire Salaam so that he attains thirty good deeds. The least reward for a good deed is ten times its like; therefore, by saying the full greeting, one can earn three hundred good deeds or more. Accustom yourself to completing the Salaam up to 'Barakaatuh' to obtain this great reward.
The Muslim says the Salaam many times during the day. He says it when entering the Masjid to the people sitting and when leaving them,  entering and leaving his house etc.
Do not forget that it is also from the Sunnah that whoever decides to leave a person that he should say the complete Salaam:
When one of you comes to a gathering, then say: 'Salaam,' and if someone decides to leave, then say: 'Salaam,' and the first does not have more right than the last. 
as the Prophet (PBUH) said: Do not consider any of good things as insignificant - even if it that you meet your brother with a cheerful face.
4. Shake hands, as the Prophet (PBUH) said:
There are not two Muslims who meet each other and shake hands, except that they are forgiven before they depart (from each other).
Imaam An-Nawawee said:
Know that this shaking of hands is preferred with every meeting.
Notice that if you shake hands with whomever you meet, greet them with Salaam and smile at them you would have fulfilled three Sunan at once.
''Say to my Slaves to say that which is better. Verily, shaytaan incites to evil between them. Verily, Shaytaan is for mankind clear enemy.''
The Prophet (PBUH) said:
A Kalimah Tayyibah is charity.
Kalimah Tayyibah includes the remembrance of Allah, supplication, Salaam, praising someone for their good traits, noble character, good manners and actions.
A Kalimah Tayyibah has a powerful affect on a person - it brings peace and tranquility to a person's soul and puts serenity into his heart. It is evidence of what is in the heart of the beleiver of light, guidance and proof of being of the right path.
Have you thought, my dear brother, to fill your life - from the morning to the evening - with kind words, to your spouse, children, neighbours, friends, co-workers and whomever else you deal with, who maybe in need of such words?
 No evidence for saying the Salaam when entering or leaving the Masjid was found. However, what is confirmed in the Sunnah is to pray two Rak'aah of Tahiyaat Al-Masjid on entering.
 i.e. it is important to give Salaam when leaving or gathering, as it is when entering it. So one does not have more right than the other.
 It is not permisible to shake hands with a non-Mahram.