People mail packages to Costa Rica all the time. I have received many.
Basically, you have two choices: Mail it through the US Post Office and it will go through the Correos de Costa Rica. If the people you are sending to have a post office box (apartado) send it there. Some people do not have home delivery in remote areas so this is the best option for that.
The other choice is a private mail service such as Carga Tica mentioned by roadadvisor. This way, you mail the package to a Miami address and then Carga Tica ships it to San Jose. Usually, the recipient can make arrangements to have it sent to him some way - often on the bus - if they don't live in or near San Jose.
Sometimes packages get held up in customs - which will have to be paid - and if the package is shipped through Correos de Costa Rica, the recipient might have to go to the nearest customs location to pay the duties. Usually, the private mail service will take care of this and then you pay them.