Can my friend who is a refugee travel document holder from Spain come to the U.S. with/without a visa?
No. Your friend requires a visa to come to the US.
Citizens of Spain can come to the US without a visa under the Visa Waiver Program, but one criterion for participating in the VWP is to have the nationality of, and present a passport issued by, a VWP country (8 USC 1187(a)(2)). Your friend is therefore unable to come to the US under the VWP even if he or she has the nationality of a VWP country, because refugees are generally unable to use a passport issued by their country of nationality.
The US embassy in Spain and Andorra has a page about visas that would serve as a good starting point to get more information about how to apply.