There are two ways to build a party, since the classes have a lot of overlap: Class and Role.
Generally speaking, Class gives people an idea of what you’re doing, but a Role defines it. Sometimes a cleric uses a crossbow, sometimes a rogue uses magic. A role lets the others know what you’re doing.
Archmages are your general nukers, crowd control and AoE damagers. This is your man who solves problems with magic, often through a giant explosion of it. Defined most broadly as a “backline” caster who has little to no AC. Arcanists, wizards, witches, shamans, sorcerers, and druids often are archmages.
Champions are the team captain and damage dealer. The Champion leads the charge and is generally hitting as hard as he can, either as DPS or a DPS/tank. Barbarians, fighters, gunslingers, inquisitors, slayers, swashbucklers, and bloodragers are among those who often fill this role.
Guardians are those who occupy a foe’s attention, either by tanking, distracting, or disabling. Tripping, challenges, disarming, quarries, repositions… these are the tools of the Guardian; he keeps the baddies away from the back line of the party and from killing the Champion or Trickster. Monks, fighters, paladins, cavaliers, brawlers, druids, and skalds often fill this role.
Hierophants are healers and buffers/debuffers; they generally have area effects which aid their allies, cast healing magic to keep the party on their feet, and create empowering boons to accentuate a strength. A hierophant provides areas of safety, as well as elemental protections and wards; they should really come across as a first aid kit, prepared to fix any manner of flagging weakness in their allies. Cleric, bard, druid, oracle, witch, shaman, and warpriest cover the role most often.
Tricksters are those who want to remain out of the melee press until they deal their massive damage. They can disable foes by striking a hard-to-target weakness, undermine a foe’s advantage, and provide overwhelming DPS. Tricksters are often not able to take many hits, so they rely upon the Champion and Guardian. Rogue, investigator, magus, alchemist, gunslinger, bard, and inquisitor are among those who cover the Trickster role.