Changes
The change in debt-to-GDP is approximately "net increase or (decrease) in debt as percentage of GDP"; for government debt, this is deficit or (surplus) as percentage of GDP.
This is only approximate as GDP changes from year to year, but generally year-on-year GDP changes are small (say, 3%), and thus this is approximately correct.
However, in the presence of significant inflation, or particularly hyperinflation, GDP may increase rapidly in nominal terms; if debt is nominal, then its ratio to GDP will decrease rapidly. A period of deflation would have the opposite effect.
Read more about this topic: Debt-to-GDP Ratio