I think it is safe to say that when talking about the debt of a sovereign nation that we can agree that it is quite different than say personal or business debt at very fundamental levels. With that being said there are a number of policies that can be enacted to reduce a number of debts. The first two are obvious.
Raise Taxes: The most obvious way to pay off debts is to increase revenue and this can be done by raising or levying new taxes or tariffs. Increasing additional revenue to apply to the debt for it to be paid down will decrease the overall number. The political advantages of this are that you can reduce debt without making difficult political decisions about which budgets and funds to slash. The cons are that nobody likes having their taxes raised and can be politically unpopular.
Cut budgets: Governments usually form a budget that allocates a fixed amount to various programs or services for the year. More money will be left over if those budgets are slashed and can be applied to debts. Pros are that you help lower debts without raising anybodies taxes. Cons are that you are negatively hurting programs and services and that can be politically unpopular.
Print More Money: Money is typically issued by governments, and despite the fact that it doesn't necessarily need to be backed by anything to have value, people still seek to accumulate it. To understand why people want money, and why people accept a governments money as currency is quite simple. The government simply has to state that all taxes due to the government must be paid using this currency. The fact that people must have the government money to pay their required taxes makes it universally valuable and accepted by the nations economy. Now the government simply has to print money and use it to fund its various spending for it to be circulated through the economy.
The pros of this is that the government can spur economic activity in the short term simply by printing money for its spending and debt reductions. This spent money encourages companies to form, puts people to work who otherwise might not be working and can sometimes be the necessary adrenaline shot the economy needs. A good example are the quantitative easing programs currently run by the Fed right now. The cons of this however is that this can be harmful to the economy as a whole in the longer term as every printed dollar requires the economy to continue growing relative to the rate of printing money, otherwise inflation occurs.
In a stagnant economy, inflation can run rampant as the value of the currency drops, each dollar applied to reductions of debt comes at the collective cost of every member of the economy. A good example of this is the Weimar Republic of Germany, that was under such crushing foreign debt after the first World War that it began to print money out of control to pay off this debt. Their currency became worthless and the economy had the wealth sucked out of it so to speak.
Float Bonds: This is essentially a way to borrow money from one source to pay off liabilities or debts elsewhere. It is also the primary way that the United States issues new currency through the Federal Reserve. They do not simply print money directly but instead sell bonds to the Federal Reserve in exchange for the currency it needs to pay off other debts.
Start a war/Nationalize foreign assets: One convenient way to handle absolving all the debt that you owe a particular nation is to start a war with them. One of the first things that happen in war time are the foreign assets of that country are nationalized and all foreign debts are forfeited. The pros are that you can simply give the middle finger to your debtor and bomb them. The con is obviously war. Notable examples are the rise of the Nazi party in Germany and how they essentially started a giant war to escape the old foreign debts from the other European countries, we see how well that turned out for them though. Another notable example would be the ancient Rome. They would accumulate debts with other nations to fund their military, then use that same military to conquer that nation and absolve their debts, and then in turn make their people tax paying Roman citizens.