With examples from Saiyuki and Pride and Prejudice and Zombies.
To party is a regular verb, meaning it takes a standard -ed ending in the past tense, and it generally means to attend a party; to have a good time or even to take drugs or drink alcohol (usually with others in a social context). And, as with other regular verbs ending in -y, we change the Y to an I when we shift into past tense:
Hakkai allowed himself a satisfied smile as he whipped open the curtains to let in the painfully bright morning light.
"Have a heart, Hakkai," Gojyo groaned. "I partied pretty hard last night, and I'm feeling kinda rough."
It can also mean to entertain at a party; to accompany to a party:
Gojyo couldn't believe the stupid monk's luck. Every monastery and village across China had partied him, just because he was a high-and-mighty Sanzo priest. They sure as hell didn't do it because of his personality.
But "partying" didn't always mean having a good time (or too much of a good time, as in Gojyo's case). Interestingly, the verb to party used to have more varied meanings than it does today. For instance, "to party" could mean to take the part of, side with. This meaning is now obsolete, but if you're writing for an English-language fandom set before 1800 or so, it's fair game:
Elizabeth Bennett drew her katana and stepped forward to meet the oncoming horde of shambling, moaning unmentionables. "Those of you who partied me during the debate last night at Mrs. Foster's ill-fated ball, promising you would stand fast against the undead, follow! We must answer England's noble call and grant sweet, true death to these poor souls!"
Although Lizzie is talking about a party she attended, she's not using partied in the modern sense of having a good time. She's actually referencing a discussion that took place at the Fosters' soiree, which—knowing her—she and her supporters probably won.
No matter which meaning you're interested in, though, the past tense of to party remains the same. Just put an -ed ending on it and make sure you've changed the Y to an I, and you're good to go.
"Party" (Oxford Dictionaries)
"Party, v." (Oxford English Dictionary online) Note: You need a subscription to be able to access this entry on the OED online.