system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: How do engagement rings work?

Kind of never learned that part when I was young.
So how is this process work? after a man gives a woman the ring, she carries it with her and then takes it off on the wedding day? do the couple go for ring shopping after the proposal to find a ring for the man? I've seen people put their wedding ring on both left and right hand, does it matter?

Thanks.
gpt
Short version:  Do whatever makes the two of you happy.

Long version:  Emily Post documented the rules of polite society in the 1920s.  It has been the standard of American tradition.  For very formal couples or people with an eye to please their elders, this might be a useful read:

 
 

>THE ENGAGEMENT RING

  >It is doubtful if he who carries a solitaire ring enclosed in a little square box and produces it from his pocket upon the instant that she says “Yes,” exists outside of the moving pictures! As a matter of fact, the accepted suitor usually consults his betrothed’s taste—which of course may be gratified or greatly modified, according to the length of his purse—or he may, without consulting her, buy what ring he chooses. A solitaire diamond is the conventional emblem of “the singleness and endurability of the one love in his life,” and the stone is supposed to be “pure and flawless” as the bride herself, and their future together—or sentiments equally beautiful. There is also sentiment for a sapphire’s “depth of true blue.” Pearls are supposed to mean tears; emeralds, jealousy; opals, the essence of bad luck; but the ruby stands for warmth and ardor: all of which it is needless to say is purest unfounded superstition.   10 
>  In the present day, precious stones having soared far out of reach of all but the really rich, fashion rather prefers a large semi-precious one to a microscopic diamond. “Fashion,” however, is merely momentary and local, and the great majority will probably always consider a diamond the only ring to have.   11 
>  It is not obligatory, or even customary, for the girl to give the man an engagement present, but there is no impropriety in her doing so if she wants to, and any of the following articles would be suitable: A pair of cuff links, or waist-coat buttons, or a watch chain, or a key chain, or a cigarette case. Probably because the giving of an engagement ring is his particular province, she very rarely gives him a ring or, in fact, any present at all.   12 
>  The engagement ring is worn for the first time “in public” on the day of the announcement. 


>BUYING THE WEDDING RING

>  It is quite usual for the bride to go with the groom when he buys the wedding ring, the reason being that as it stays for life on her finger, she should be allowed to choose the width and weight she likes and the size she finds comfortable.