-- Are you going to party this weekend? -- Partying this weekend? -- Did you party hard with the guys last weekend? -- Do a lot of partying on your vacation?
-- We're planning on partying like crazy on this summer on Ios [famous Greek partying island in the Cyclades].
To party, as I've understood it, doesn't necessarily mean to go to (organized) parties, but rather to engage in activities the main or sole purpose of which is to have fun. Often this involving various substances. So, going to a baseball game would NOT be considered partying (even though it's hopefully fun), but going drinking with your buddies afterward would. If you drank a lot convivially with tus amigos (or even strangers) at the game, then you could say: "We really started to party by the third inning."