There are a number of different collections of Islamic terms and common expressions. Here is a collection that I have found to be most useful to explain common expressions and terminology used by Muslims.
 

ALAYHIS SALAM-
'Peace be upon him', a formula used after the name of a prophet


ALLAHU AKBAR-
The Arabic expression meaning 'Allah is greater.' Also called the takbir


ALLAHU ALAM-
An Arabic expression meaning 'Allah knows best'


AMMA BAAD-
An expression used for separating an introductory from the main topics in a speech; the introductory being usually concerned with Allahs praises and glorification. Literally it means 'whatever comes after'


ASTAGFURALLAH-
The Arabic expression meaning 'I ask forgiveness of Allah'


AUDHU BILLAHI MIN ASH SHAYTAN AR RAJIM-
The Arabic expression meaning 'I seek protection in Allah from the accursed satan.'


AZZA WA JAL-
A formula used after the mentioning the name of Allah meaning 'Mighty and Majestic is He'


BARAKALLAH FIK-
An expression which means 'May the blessings of Allah be upon you.' When a muslims wants to thank another person, he uses different statements to express his thanks, appreciation and gratitude. One of them is BarakAllah


BISMILLAH AR RAHMAN AR RAHIM-
The basmala. 'In the name of Allah, the all Merciful the all Compassionate.'
[this is also translated as in the name of Allah most gracious most merciful]


FI AMANALLAH-
Valedictory phrase meaning 'In Allahs protection'


FI SABILILLAH-
The Arabic expression meaning 'In the way of Allah', 'For the cause of Allah' [also used to mean 'for the love of Allah']


AL HAMDU LILAH WA SHUKRU LILLAH-
The Arabic expression meaning which means 'Praise belongs to Allah and all thanks to Allah'


HASBALA-
The Arabic expression, 'Hasbunallah wa nimalwakil' meaning 'Allah is enough for us and an excellent guardian'


HAWQALA-
The Arabic expression, 'la hawla wa la quwwata illa billah' which means 'There is no power nor strength save (expect) by Allah'


INNA LILLAHI WA INNA ILAYHI RAJIUN-
This is something which a muslim expresses when he is afflicted by a misfortune, the meaning of which is 'We are from Allah and to Him are we returning.' It is taken from an ayat (verse) from the Quran (ch 2 vs 156).
[this is usually said upon hearing of the death of an individual]


INSHALLAH-
The Arabic expression meaning 'If Allah wills'
[this is usually said when referring to a situation in the future e.g. inshAllah I will go to the grocery shop tomorrow etc]


ISTIGHFAR-
To ask the forgiveness of Allah, especially by saying, Astagfuralah, 'I seek the forgiveness of Allah'


ISTITHNA-
Exception, saying 'InshAllah', 'If Allah wills'


JALLA JALALUH-
The formula said after the name of Allah meaning 'Great is His Majesty'


JAZAKALLAHU KHAIRAN-
This is a statement of thanks and appreciation to be said to a person who does a favour. Instead of saying 'shukran' (thanks), this phrase is used. It means 'May Allah reward you with good.


KARAM ALLAHU WAJHAHU-
'May Allah honour him', a formula used when Ali ibn Abi Talib (RadiAllahu Ta'ala anhu) is mentioned


LABBAYK-
'At your service', the talbiya or call of the pilgrim to his Lord in the hajj.

[the full talbiya is 'LabbaykAllah huma Labbayk, LabbaykAllah sharee kalala Labbayk, innal hamda, wa naimata lakawulmulk la shareekala' which means "Here I am O Lord, here I am, Oh Allah, here I am. Here I am. You have no partner. Here I am. Surely all praise, grace and dominion is yours, and you have no partner."]


LA HAWLA WALA QUWWATA ILLA BILLAH-
The meaning of this expression is 'There is no power nor strength save in Allah'. This is said by a muslim when he is struck with calamity, or is taken over by a situation beyond his control.


LI WAJHILLAH-
Literally, 'For the face of Allah', meaning in order to obtain the pleasure of Allah, purely for Allah himself.


MA SALAMA-
'With peace', a formula for ending letters


MASHALLAH-
A phrase literally meaning 'What Allah wishes', and it indicates a good omen
[example of usage, I get an A in a test, my mother would say MashAllah]


MALWANA
'Our master', a term of respect
[usually used in the context of referring to the Prophet , also however used in the context of referring to a learned individual e.g. scholar or imam, a concept I am not too keen on supporting and Allah knows best]


RABBANA WA LAKAL_HAMD-
'Our Lord, Praise if yours', said after rising from ruku after saying 'sami Allahuliman hamidah'
[which means 'Allah listens to the one who praises him']


RADIYALLAHU ANHA-
The formula 'May Allah be pleased with her' used after a female companion
[usually abbreviated as RA or RAA]


RADIYALLAHU ANHU-
This is an expression to be used by muslims whenever a name of a companion of the Prophet Muhammed is mentioned or used in writing. IT means 'May Allah be pleased with him'
[usually abbreviated as RA or RAA]


RADIYALLAHU ANHUM-
The formula, 'May Allah be pleased with them', used after a group of companions
[usually abbreviated as RA or RAA]


RAHIMAHULLAH-
The formula, 'May Allah have mercy on him'


ASSALAMU ALAYKUM
'Peace be upon you' the greeting of the muslim
[the reply is 'wa alaikumus salam' which means 'and peace be upon you. The fuller version reads, 'assalam u alaikum wa rahmatulahi wa baakatuhu' which means 'peace be upon you and the blessings and mercy of Alllah' the reply is 'wa alaikumus salam wa rahmatulahi wa baakatuhu']


SALLAHU ALAYHI WA SALLAM-
'May Allah bless him and grant him peace', the formula spoken after the mentioning of the Prophet Muhammed
[usually the following two sets of abbreviations are used for this phrase (pbuh) which means 'peace be upon him' and is the technical reply for all Prophets or (saws) the correct suffix when referring to the Prophet Muhammed ]


SAMI ALLAHU LIMAN HAMIDAH-
'Allah heard him who send praise to Him', said by someone praying when he rises from ruku (unless he is following an imam in prayer)
[if he is following an imam in prayer he says 'Rabana wala kalhamd' only]


SAYYIDUNA-
'Our Master', a term of respect
[usually used to refer to the Prophet Muhammed , however many people use it to refer to learned man / scholar, a practise I am not keen on - and Allah knows best]


SUBHANALLAH-
'Glorified is Allah.' To honour Allah andmake Him free from all (unsuitable evil things) that are ascribed to Him, (or 'Glorified be Allah')


SUBHANAHU WA TA'ALA-
'Glorified is He and exalted,' an expression that muslims use when the name of Allah is pronounced or written
[this us usually abbreviated as (swt)]


TA'ALA-
'Exalted is He', an expression used after the name of Allah is mentioned
[i.e. Allah Ta'ala meaning, Allah, exalted be He]


TAAWWUDH-
Saying, 'I seek refuge in Allah...' (audhu billahi minash shaitan nirajeem)


TABARAKALLAH-
The formula 'Blessed is Allah'


TAHMID-
Saying the expression 'alhamdulillah', which means 'Praise belongs to Allah'


TAKBIR-
Saying 'Allahu akbar', which means 'Allah is Great'


TALBIYA-
Saying 'Labbayk', which means 'At your service' during the hajj


TAMJID-
Glorifying Allah


TARDIYA-
Saying one of the expressions which begin with 'radiyallahu....'


TASBIH-
Glorification, saying 'SubhanAllah', which means 'Glory be to Allah'


TASHMIT -
Uttering a prayer for the sneezer which thes the form, 'yarhamuk Allah' which means 'may Allah have mercy on you'
[when a person sneezes he says, Ahamdulillah (Praise be to Allah), a person who hears the sneeze says 'yarhamuk Allah' and the sneezer replies 'Yahdikumul-lah wa Yuslih balakum' which means 'May Allah give you guidance and improve your condition.']


WAJHULLAH -
'The face of Allah', meaning for the sake of Allah, irrespective of any reward in this life, purely for Allah'