When arabic words are transliterated, how do you know what letters are silent? For example, to me "astaghfirullah" would sound exactly as it looks it does. Yet, hearing it said, it always seems the first a is dropped off and the word is "staghfirullah". 

Same with nargileh...I asked a Lebanese friend how to properly pronouce it and he said it's actually argileh. 

With "moon letters" (الحروف القمرية), however, the definite article is not assimilated into the following letter.
أ (a) الأخ (il-ax) the brother
القهوة (il-'ahwa) the coffee
ب (b) الباب (il-baab) the door
ح (H) الحفلة (il-Hafla) the party
خ (x) الخضار (il-xoDaar) vegetables
ع (3) العربية (il-3arabiyya) the car
غ (ġ) الغدا (il-ġada) lunch
ف (f) الفندق (il-fundu') the hotel
ق (q) القرية (il-qariya) the village
م (m) المية (il-mayya) the water
و (w) الوادي (il-waadi) the valley
ه (h) الهدية (il-hidiyya) the present
ي (y) اليونان (il-yunaan) Greece

I hope the above explain is useful for you and If you have any questions don't hesitate to ask .
and you are welcome

Dear Cayce
Thanks for your question . Before anything we need to see how to write "astaghfirullah" in Arabic.
استغفر الله
It's two words Allah and my request from Allah. This word "استغفر الله" means I ask Allah for forgiveness.
Every letter in this word must pronounce and there's not silent letter.
In Arabic you can't find silent letters only on thing Sun and moon letters..
I'm going to explain it as the following :

If a word begins with one of the "sun letters" (الحروف الشمسية), and is definite, the "l" of the definite article is assimilated into the following consonant. So instead of pronouncing الشمس as "il-šams," you say "iš-šams.

ت (t) التمن (it-taman) the price
ط (T) الطالب (iT-Taalib) the student
د (d) الدنيا (id-duniya) the world
ض (D) الضيف (iD-Deif) the guest
س (s) الست (is-sitt) the woman
ص (S) الصيف (iS-Seif) summer
ش (š) الشركة (iš-šerka) the company
ز (z) الزيت (iz-zeit) oil
ظ (Z) الظرف (iZ-Zarf) the envelope
ج (ž) (the French "j") الجاكيتة (iž-žakitta) the jacket
ن (n) النور (in-nuur) the light
ر (r) الراجل (ir-raagil) the man

In Egyptian Arabic, there are two more letters that may or may not be assimilated:
ج (g) الجمل (ig-gamal or il-gamal) the camel
ك (k) الكتاب (ik-kitaab or il-kitaab) the book

When arabic words are transliterated, how do you know what letters are silent? For example, to me "astaghfirullah" would sound exactly as it looks it does. Yet, hearing it said, it always seems the first a is dropped off and the word is "staghfirullah". 

Same with nargileh...I asked a Lebanese friend how to properly pronouce it and he said it's actually argileh. 

When arabic words are transliterated, how do you know what letters are silent? For example, to me "astaghfirullah" would sound exactly as it looks it does. Yet, hearing it said, it always seems the first a is dropped off and the word is "staghfirullah". 

Same with nargileh...I asked a Lebanese friend how to properly pronouce it and he said it's actually argileh.