I know the first year is the original cost minus the salvage value, divided by the years of useful life. How is the last month calculated?

Say the original cost of a truck is $8,500 and minus a salvage value of $1,000, divided by a 5-year life. This equals $1500 for a full year, but if it was bought in May, the $1500 divided by 12 months, times 5 months equals $625. Do I just take $1500 minus $625? Or is there a more complicated answer?

Actually, you are almost right but you should multiply the $1,500 by 7 months from may to December not by 5 months. So the depreciation for the first year will be 875.