In the wedding industry, we refer to this time as "engagement season" since many couples, straight and gay, get engaged between Thanksgiving and Valentine's Day. I know that many same-sex couples have questions about who proposes and who gets the ring...
Anyone can propose marriage, but in gay relationships, it's very common for the other partner to propose back, at a separate time. So each partner gets to experience the exhilaration of being proposed to!
In my experience, many gay men will only wear one ring, not two. In this case, often the engagement ring will double as a wedding band.
Younger lesbian brides (those under 40) are likelier to wear two rings. For example, my wife Jen, like many lesbians, wears her engagement ring and wedding band next to each other on the same finger. This is very common, and of course, traditional. My engagement ring doesn't have a stone (my choice) so my engagement ring is now on the ring finger of my right hand, and my wedding band is on the ring finger of my left hand.
I've noticed that gay and lesbian couples who are older and/or who've been together for a long time, already wear rings and in this case, usually substitute those rings with new wedding bands, forgoing an engagement ring altogether. These couples are also less likely to have had a traditional "pop the question" proposal experience, hence the lack of engagement rings.
What are you doing for your engagement rings? Who popped the question?