From the Church’s MormonNewsroom.org site:
The Church of Jesus Christ of Latter-day Saints has approved an electronic method for members in the United States to pay tithing and submit other charitable donations.
The Online Donations system will allow members in the United States an additional method to submit their contributions to the Church. Historically, donation envelopes and contributions were given to priesthood leaders in each ward and branch. In the future, this same process may still be used. However, for those who wish, they may make their contributions through the online donation system developed by the Church.
The Church Online Donations website will be rolled out to congregations in the US throughout 2015, and the Church will notify local leaders when it is available in their area.
The Church’s Finance and Records Department says the initial site not only demonstrated a simplified donation process for members, but also showed that this new approach reduced the load on local leaders and clerks charged with processing donations.
And for those with a friend or family member serving a mission, the website allows anyone with an LDS Account — Church member or not — to donate to help financially support that missionary.
For Latter-day Saints, tithing is a natural and integrated aspect of their religious belief and practice. By the biblical definition, tithing is one-tenth, and Church members interpret this as a tenth of their “increase,” or income, annually. It is paid on the honor system. No one asks to see income statements or pay slips.
Tithes and other charitable donations help the Church carry out its mission of spreading the gospel of Jesus Christ, caring for the poor and strengthening members’ faith and commitment to Jesus Christ. (Learn more about tithing and charitable donations.)
Below is a screenshot of the Donations History portion of the Church Online Donations website:
Here is an introductory video: