There is not necessarily a right or wrong way to wear them, but there is a traditional way, and that is with the wedding band placed on the finger first and the ER placed on afterwards. Clearly, a lot of people do things differently, and there are even different traditions in different cultures. Wear your rings the way you wish, but people who choose not to wear a band on the left hand, for example, often face questions like, "When is the wedding?" Not that other people's perceptions are your problem, of course, just that people generally expect to see a band and then an ER on the left ring finger.
I often wear my wedding band, my ER and then an anniversary band, but recently I've been wearing my WB, AB and then my ER. It all reads mostly the same - band/s and then ER. But you would still be just as married even with no rings at all!
Since my upgrade this past Sept and December, I have been wearing my e ring on my left hand and my anniversary band on my right hand. They match, and we had the e ring done first, back in sept. DH surprised me with the anniversary band in December. The anniversary band was made wider with a larger carat weight than the e ring setting, still matching with baguettes and princess cut diamonds, but DH had that done by design. He had both custom made and was very specific with how he wanted them made. Back in sept when I only had my newly upgraded e ring, I still wore my e ring on my left hand and DH had the jeweler copy my old wedding ring from my old set to be white gold instead of yellow gold. I wore that ring on my right hand after it was finished. Nobody ever asked me when my wedding is! I just received lots of compliments. Then he surprised me with the matching anniversary band in December which is worn on my right hand. Again, I never received any questions about a wedding. We are married almost 19 years. In feb I had to give my anniversary band to the jeweler who had to re make it due to defects that were found in the metal setting. I went back to wearing my old, newly made wedding band on my right hand. I just got my beautiful anniversary band back this past Wednesday and its perfect!!!! I'm thrilled and its back on my right hand! IMO, and this is only ME because everyone feels differently, I like to have my solitaire stone that was given to me the day I was engaged on my left hand at all times. When we discussed upgrading my e ring, my original plan was to have a very wide band made that could act as a wedding band/ e ring combo. When we talked to several jewelers we were told this was a very common thing to do nowadays, as many people complained that wearing two rings wasn't comfortable and one was always spinning around. I wanted to be sure I wouldn't get those questions, being married to my DH for almost 19 years!!!!! That old wedding band that he had re made for me in white gold was my wedding band he put on my finger back in 1994, and the e ring fit in like a puzzle. When he told me he was having that band remade so I could still look down and see it everyday, I decided to wear that on my right hand as my wedding ring. When he surprised me with the anniversary band, I was shocked and thrilled! (See my avatar). Anyway, wear your rings the way you want!!! I am!!!!