I´ve tried myself, though I did not understand it all.

Yüzüğü takip senin olunca güzeldir herşey neyse boşver

My try = If you look at the face and it is yours its beautiful/all good/great whatever never mind.

Waiting for corrections! =D

Unfortunately the sentence structure is too weird for me as a learner, so I just translated the words for you

yüzük = ring (as in the ring worn on your finger)

yüzüğü = the ring or his/her ring

takip = pursuit, chase

senin olunca = when it is yours

güzeldir = it is beautiful

herşey = everything

and you correctly translated neyse, boşver

Yüzüğü takıp senin olunca güzeldir herşey neyse boşver.

devrik cümle doğrusu şöyle olmalıydı

Yüzüğü takıp senin olduğumda herşey güzel olur. Neyse boşver.

When i marry you everything will be nice, anyway nevermind.

yüzük takmak=to exchange rings, to marry

when we exchage rings and when i become yours (your spouse) everything will be nice, anyway nevermind

What makes it look weird is the place of the subject. In the sentence the subject (her şey)follows the predicate (güzeldir.) It is an inverted sentence. But this does not mean it is incorrect and needs to be corrected. All you have to do with inverted sentence is to find out the subject, and, if this helps you, put it in the beginning of the sentence:

Her şey, yüzüğü takıp senin olunca güzeldir.

It can be translated as follows:

When you get married everything is happily ever after

or

When you get married everything looks good and loving

or

When you get married everything will all be roses and honey

or (just kidding! )

When you get married everything becomes dull !

Thanks Vona, I have seen inverted sentences used in poetry, or for emphasis, but sometimes I wonder whether some people just write as the ideas come into their head, as in stream of thoughts. 

If you or someone else has the time, I am still confused by takıp in this sentence. 

I originally thought that takip was the correct spelling, for the noun.

But, does takıp mean it is a verb from takmak using the ıp suffix?

Then I looked for the final verb and only saw güzeldir (it is beautiful).

I have never seen it (the ip suffix) used in combination with the dir suffix.

An interesting thought, especially from an English speaker. Word order in English is very strict even though we hardly pay attention to it. The position of a constituent pretty much determines its function in the sentence because there are so few grammatical markers.

In Turkish "stream of thoughts" is possible because every part of the sentence is grammatically marked. One thing that guarantees us free hands is the form of compounds: you can actually place the constituents of a compound in any place you want and you still see from their forms which words belong together.

As a speaker of another agglutinative language I notice pretty much the same things but in Finnish  -  even though word order is free  -  it is always meaningful. I don´t think we can say this about Turkish: apart from the position next to the verb on the left which is stressed I cannot see what is the message non-typical word orders or devrik cümle carry. I don´t think there is any. It is just used because of lust for life I guess.

The word order rules that learners get used to  -  like placing the verb in the end in an unmarked sentence resemble those of Swedish or German to me. They are not really necessary but when used effectively they maybe lessen the effort of the listener because he knows what to expect. Works for learners at least as we see.

One thing is for sure. Inverted sentences sound very beautiful when they are not too many.

In the sentence -ip suffix is in combination with the -unca suffix : takıp senin olunca.

The -dır suffix, as you know, also used to make predicate out of noun:

güzel (noun) 

güzeldir (predicate)

Her şey güzeldir. (everything is beautiful)

takıp senin olunca is adverbial adjunct.

Her şey (yüzüğü takıp senin olunca) güzeldir.

Here are some examples for the combination of -ıp and -ınca suffixes:

Gidip bakınca 

olup bitince

sararıp solunca

düşüp kırılınca

et cetera..

Vona, açıklaman için çok teşekkürler