According to traditions a woman usually wears her engagement ring and her wedding band on the fourth digit of her left hand. The fourth finger is usually called the ring finger for plenty of reasons. The Roman culture claims the vein connected with this finger connects directly to your heart and as per the Chinese tradition the fourth finger is a symbol of your life partner. But it is not necessary that you follow these old cultures, there are numerous other ways to wear a wedding band that shows equal amount of love and dedication for your would be partner.
You can wear the wedding band on a chain. This is very convenient for woman especially as their hands are constantly exposed to harsh elements. There are many women who find it convenient weave the ring on a chain around their neck. This prevents the ring from getting lost while doing the daily chores and literally keeps the ring close to your heart. The other alternative that women go for with the wedding band is to reinvent them into a different jewellery piece. The diamonds on the wedding ring are made into earrings or may be a pendant. New stones can be added in the necklace to adorn it further.
There are many brides who also keep away the engagement ring for their sons or daughters and replace it with their wedding band. But again there are many wedding and engagement rings that come in a set. In case of this you can probably wear the wedding ring on your finger first and then put on the engagement ring. The other way is to wear either of the rings around your neck or whichever of the two rings are simpler in design you can get it resized to be worn on your thumb. But in all this remember a wedding ring is symbolic of the love between you and your spouse so you should keep it close to you all the time.