As of 2015, a good location to find the Methodist hymnal online is the Hymnary website. The hymnal offered on the site is for the United Methodist Church.
The hymnal that is offered at the Hymnary site was published in 1989. The hymnal is organized by the song title, and the site is free to use.
Another good location for a Methodist hymnal is Cokesbury. The site offers a hymnal that was published in 2001. Users of the site must create an account and pay a subscription fee before they can gain access to the hymns. Search options allow hymns to be found by scripture, topics and key.