Hi,
The 4th answer by "Si++" seemed to be the most appropriate to me, but I also want to contribute with my own thoughts...
There are a few points, you should consider here...First of all,
a) Turkish language has this strange habit of using "past tense" with adjective forms regardless of the tense they refer to (except for future cases). For example,
Sevdigim adam = The man I love
So, in spite of the past "-di" suffix, it usually refers to a general case (aorist tense, or simple present). But it can very well refer to the past tense.
Gordugum adam = The man I saw
Such connotations are understood from the context but can still be clarified with additional details or a higher level tense. For example,
Sevmis oldugum adam = The man I (had) loved, or
Onceden sevdigim adam = The man who I´d loved before
b) Using the "-digi" form, as in "oldugu", requires you
i) to convert the tense into past if not already,
ii) put the verb before the noun (reorder the sentence, as in an adjective clause)
iii) add "-gi) suffix between the tense suffix (-di) and the personal suffix (like -m).
The ending result would be "gordugum, gordugun, gordugu etc...). This structure essentially implies "noun who/which/where/when subject (I/you/he etc) verb"
Examples :
Araba aldim = I bought a car
Aldigim araba = The car (which) I bought (put "gi" as in aldi-gi-m, and rearrange)
O kizi seviyorum = I love that girl
Sevdigim kiz = The girl I love (Change seviyorum to sevdim, put gi in between, rearrange)
c) Turkish also has "to be verb", simply "olmak", which also complies with the past tense rules stated above. When used as an adjective, the to be verb must be changed to the past tense.
Examples
Diyorum ki, "Sen cok guzelsin". => I say, "You are so beautiful".
Cok guzel oldugunu soyluyorum. => I´m telling you that you are so beautiful
The second sentence uses the adjective form, so it has to comply with all the rules above.
- First the "to be" verb suffix "-sin" changes to the past form "oldun".
- Second, the -gi suffix is added in between "du" and "n" (with vowel harmony in action), ending up with "oldugun".
- So the phrase "cok guzel oldugun" means "that you are so beautiful". It needs the "-i" suffix to indicate the "direct object" (becomes -u here).
The to be verb is a bit tricky in Turkish. Check this out,
Cok guzelsin => You are so beautiful
Cok guzeldin => You were so beautiful.
Funny thing is that, the "olmak" verb is hidden there (just like the to be verb would be). However, when you want to phrase it as above, you have to use it to enable the usage of suffix (-gi). Otherwise, the compare the two sentences
Cok guzel oldugun => That you are/were so beautiful
Cok guzel oldun => You´ve become so beautiful (not you were so beatiful)
d) The gerund form (such as "olma, olmasi, olmam" etc) is used in certain other situations.
I would suggest you think simple to better understand Turkish. It´s extremely logical but also simple (not necessarily easy!). The same principle applies here.
- if you can easily rephrase the sentence with "that" (without further manipulation), use the "-gi" phrase (like oldugu), generally the noun clauses as secondary sentences.
- if it is the primary sentence and/or cannot be manipulated by "that" or another clause instrument like "what/which/what/who" etc, then you use the gerund form, as in "olmasi".
Examples:
You need to come tomorrow => Yarin gelmen gerekiyor. (no clause instrument!)
Ne oldugunu bilmiyorum => I don´t know what happened (note the "what").
I didn´t know that I needed to come => Gelmem gerektigini bilmiyordum.
Note that, in the third sentence, the part with "that" is translated using "gerektigi" (that I needed) while the primary part of the sentence "gelmem gerekiyor", I need to come, is translated using gerund.
Last, please don´t think
"en sevdiğim renk" as "my most-loved color", but rather as "the color that I like the most"
Because, look at that example...
En cok, bu rengi severim. => I like this color the most (literal, just upside down!)
En cok sevdigim renk => The color that I like the most (literal, just reordered for adj.)
As you see, it also complies with the rules I´d mentioned. Transform to past tense and integrate ´-gi" (meaning "that"), and put it before the noun. that´s it.
In short, For better understanding of Turkish, think simple and Turkish! 
Çok geç geldiğim biliyorum, ama bir şey söylemem gerekiyordu. Yani, ´güzelsin´ olmaktan gelmiyor. Aslında, Türkçe´de ´imek´ var. İmek olmak ile aynı anlama geliyor , ama İmek genellikle isimlerle ya da sıfatlarla kullanılır. Mesela ´Zeki isen, çok para kazanacaksın´, ´Genç idim, ama yaşlıyım artık´. Umarım birisi için yardımcı olur. İf someone wants to get an explanation in English, either PM me or comment here.
