Edited by: Destination SkillQueue on 17/10/2010 18:36:29
Corp standings is the one that counts. Missioning is the main way to do it, so you will need to fly some kind of mission. Blitzing kill missions or flying courier missions is propably the fastest way to raise your standings. Do the one that fits your playstyle and playing activity the best. Lvl 2-3 combat missions are usually really fast to blitz with no danger, courier missions take more time, but you don't have to stay at the screen or actively play to do them.
Be sure to also have a storyline agent of the corp you want to raise your standings for near you. You get higher standings boost from storyline missions, so it helps if it too is from the same corp you do the normal missions for. If the storyline agent is from a different corp and you are only interested in raising corp standings, just ignore the storyline mission given. The next time you get one it will guide you to the next nearest storyline agent and with luck it is from the corp you grind the standings for. Repeat the process until you get one for the corp in question.
For one time boosts to standings you can also look in to these. They are more focused on factions standings, so not that useful for you:Data centers
offer an alternative option to help boost your faction standings.COSMOS agents
offer another alternative way to boost standings, both corp and faction, and give more interesting rewards.