Fill a pair of pantyhose with calcium chloride tablets. Tie the top of the pantyhose off to prevent the tablets from spilling out. You can use multiple pairs of pantyhose if you want to melt a large section of frozen gutters.
Lay the pantyhose flat onto the roof. The feet of the pantyhose should rest directly on the top of the ice dam inside the gutter.
Clear the jam inside the gutter, if possible. If the gutter remains blocked, then the water is not going to have anywhere to go and the ice dam will re-form. The jam might not be locatable or might be frozen in place and almost impossible to remove. If you cannot remove the blockage, disconnect the top segment of the vertical part of the gutter from the rest of the gutters. The water can fall through this hole without needing to unclog the vertical section of the gutter.
Remove the pantyhose after the ice dam melts and there is a clear path for water to flow through the gutter. The calcium chloride is no longer needed at this point.