Fly from asia to South America.

You just need to go online and find websites that give information on cheap airfares. There are hundreds of them. They compare flights and get you the cheapest deal.
No one country is cheaper than another in Asia. It all depends on which of the cheaper airlines use what country.

I think you will find it difficult to find direct flights from Asia to Peru. You may have to transit through another country.

hi Seeb,
The price will depend a lot on the country u choose for destination, having local airlines on agreement with the international big airlines for connections.
On my last trip China to Argentina I went by Emirates as it was the cheapest option at the time (about 20.000rmb).
You can find the cheapest connection using sites like ctrip.com or edreams.es, to see what is available from your nearest asian airport to Lima. Then use a local airline in Peru for in-country connections.

Buen Viaje!