What is difference between yapılmış and yapıldı?

more examples:

bulunmuş vs bulundu

kırılmış vs kırıldı 

söylenmiş vs söylendi

alınmış vs alındı

Kabul edilmiş vs Kabul edildi

Reddedilmiş vs Reddedildi

Both of them are past. Both of them are passive. The differences are:

When the verb ends with -mış it means you have heard it but you havent witnessed it.

When the verb ends with -dı it means you have witnessed it.

The other difference is you can use a verb ends with -mış as an adjective but you cant use a verb ends with -dı as an adjactive.

Ex: Kırılmış bardak  broken glass

Hazırlanmış bir yere gidiyor gibisin.

How would you translate this sentence above?

Also i saw word patlamış mısır (popcorn). What does it mean patlamış? Why it is not patlanmış like it is hazırlanmış and not hazırlamış?

yapılmış = it has been done

yapıldı = it was done

Can you also give me few example with patlanmış and hazırlamış just to see difference?

I think you mean "patlamış". Patlanmış makes no sense. 

Examples;

Patlamış mısır

Dün hava patlamış ve deniz köpürmüştü.

Arabanın freni patlamış.

Geçen yıl bu zamanlar pantalon satışları patlamıştı.

Annem sofrayı hazırlamış.

Kendini mücadeleye hazırlamış.

Toplantı için sunumu hazırlamış.

Etc...

If you use the ones which has "-miş" as predicate, it expresses the situation/event has been learnt from someone or somewhere. When you use -miş, one understands you are not too sure, because you have learnt later.

Arkadaşlık isteğimi kabul etti. (She accepted my friendship request.)

You saw it yourself.

A tells B : Arkadaşlık isteğimi kabul etti.

B transfers this to C : Arkadaşlık isteğini kabul etmiş. (She has accepted his friendship request.)

C understands that B has learnt this after this had happened. The knowledge doesn´t belong to B.

A tells B : Bugün hiç kitap okumadım. (I have never read any book today.)

B transfers this to C : A bugün hiç kitap okumamış. (A has never read any book today.)

C understands someone else has told B about this. The knowledge isn´t his own.

example situation:

A is watching TV. He hears at the news "Önümüzdeki üç gün boyunca yağmur yağacak. (It will rain during next three days.)" When B comes home, A transfers this knowledge "Önümüzdeki üç gün boyunca yağmur yağacakmış. (It will rain during next three days.)"

B understands A has learnt this from the tv or internet or newspaper or someone else.

http://www.turkishclass.com/turkish_lesson_270

Yeterli olmadıysa daha fazla örnek yazmaya çalışırım. (I try to write more examples if this is not enough.)

Making "patlamak" passive doesnt make sense. Because it has to be always active. But after you make it causitive with adding-t suffix then you can make it passive.

patla -t -mak means "to make (something) pop"

patlatılmış means "something has been made pop"

Ex: Arabanın lastikleri patlatılmış.

The wheels of car has been blew out ( by someone)

Note: patlamak have many meanings.

Tamam, hepinize teşekkür ederim