Congratulations on your first DX or important US contact! You may already have a QSL card made and you are wondering how to go about getting a card from the DX station to confirm your contact.
I think that Green Stamps are the best way to go. There are a few countries where its illegal to accept US currency but you can use green stamps (USD bills) for 99% of what you¹ll ever QSL and they are easier for many folks outside the US than an IRC would be.
Its important to properly package and seal a QSL with green stamps to avoid postal theft which is, unfortunately, common in many parts of the world. We use a system consisting of an envelope in an envelope.
Note the taping of the outside envelope including the corners – this is an important deterrent to postal theft. Also note that the double envelope makes it nearly impossible to see that there are $$ inside. Also note how the $$ bills are folded and spaced around the QSL card to make the final result appear thin.
US QSLs or QSLs to stations with US QSL managers are simpler. You just include an SASE in lieu of green stamps. We get about a 70% return QSL rate on our direct QSLs this way which is very good. All of these steps are designed to reduce the likelihood of postal theft.
You should also get up on Logbook of the World (LoTW) and Clublog. These are two sites that can make confirming contacts easier, faster and less expense. LoTW is an ARRL tool that used a double-blind system (neither party knows what it the other¹s logs). LoTW confirmations are accepted by the ARRL for all of their awards (DXCC, WAS, VUCC, etc). You don¹t get a card but you can apply these confirmations to ARRL awards. Clublog offers an online log checking and QSL request service. Our club call (N1FD) has our logs on Clublog for example and you can request a card via the QSL or via direct mail (for a fee to cover postage). Most of the major Expeditions and many special events as well as individual operators use Clublog so you can tell if you are “in the log” and a subset will provide OQRS (online card requests) as described above. I would also recommend subscribing to the W1 Bureau. This path is slow (sometimes getting a card takes 2 years, almost never less than 6 mo) but the cost of QSL¹ing this way is very low. Not all HAMs subscribe to the worldwide Bureau system and not all countries have a QSL Bureau but most do.