To be promoted throughout the builder ranks (crafter, engineer, etc) just play the game, have fun, be nice, help others, don't break the rules, and you'll eventually get promotions. Promotions are random. If you want to ensure you don't get promoted, ask us to promote you.
For staff ranks, there is a forum to apply (please only apply once), and I read all applications before promoting, but please understand a LOT of people want to be staff. Just because you're not picked doesn't mean we don't like you.
Builder - A lot. Not sure if I'm going to list all these. You can use /help and sift through them.
Crafter - All builder commands, plus /lb me, /etree, /me, /recipe, /backpack (1 row), can capture pigs and spiders
Engineer - All crafter commands, plus /ebigtree, /hat, /backpack (2 rows), can create bridges, gates, and switch paintings with the scroll wheel, can capture pigs, cows, and zombies
Contractor - All engineer commands, plus /top, /jump, /backpack (3 rows), can capture pigs, cows, sheep, and skeletons
Executive - All contractor commands, plus the ability to use TNT and Lava, /backpack (4 rows), can capture pigs, cows, sheep, chickens, and creepers
Minimod - All builder commands, plus /jump, /kick, /mute, /jail, /lb me, /me, /backpack (6 rows), /a, can use bridges, gates, and change paintings with the mouse wheel, can capture pigs and spiders
Mod - All minimod commands, plus /ban, /tp, can capture pigs, cows, and zombies
Modmin - All mod commands, plus /invsee (can't modify), /fly, /hat, /tphere, /lb rollback, /lb tp, /tppos, /co rollback, /co restore, /whois, can capture pigs, cows, sheep, and skeletons
Admin - All Modmin commands, plus /vanish, /espawner, /clearinventory (others and self), /tptoggle, /invsee and modify, /more, full control over factions, /broadcast, /gm, /lb tp (ask