EVE New Citizens Q&A

First, train the skill Diplomacy (it's under the Social group) to as high as you feel comfortable (3-4). This will modify your "bad" standings with the Caldari upwards, perhaps to the point where it's easier for you to find better Caldari agents.

Second, if you pick an agent from a Caldari corp and do missions, you will get standings with the agent, and with the Caldari corp. This will unlock higher level agents within that corp. However, these missions don't give you Caldari State standings.

Every 16 mission that you do for the agent above (or any other agent), you will get an offer for an "Important" or "Storyline" mission, from a different agent in a nearby system. You should get a notification mail, and your Missions Journal will list the details of the mission offer. This offer will come with warnings in the text that it will affect your Caldari State standings. This is the mission that you need to do to increase your standings with the whole Caldari State, rather than just with the corp above.

So, bottom line, you grind 16 missions and then you do 1 mission that increases your Caldari standings, then repeat.

Also be aware that the 4 empires are linked; Caldari and Amarr are allied, and enemies of Gallente and Minmatar (who are also allied). So that 1 mission that will increase your Caldari standing will also increase your Amarr standing, and will decrease your Gallente and Minmatar standings.

The best way to avoid losing standings with an empire, if you do missions, is to decline missions that ask you to kill Navy personnel of the opposite empire. If the mission sends you after pirates or mercenaries or rogue drones, go for it. If it sends you to kill Gallente Navy or Amarr Navy, decline it. You can decline 1 mission per agent per 4-hour period with no penalties, so the best way to do it is to find 3-4 agents that are near each other, and if one gives you a Navy mission, decline it and switch to a nearby agent for 4 hours. With 3-4 agents available, it's unlikely that they'll all send you after Navy missions within the 4 hours that you have to wait.

If you need to verify the affiliations of the agent, corp, or empire that you're doing missions for, just right-click the agent and choose Show Info. Next to his/her portrait there should be a logo picture for the agent's corp. Click that, and it will open the show info page for the corp. Next to the corp logo there will be a logo for the empire that the corporation belongs to. Hopefully you see the C emblem of the Caldari State, but in any case if you click on that logo you should see the Show Info page for the entire Caldari State. And one of the tabs in that information window is Member Corps, where you can see ALL the corporations that belong to Caldari. You can click the blue ? Show Info button on any of them and you'll see the corp info and all the agents in that corp.

Or, you can use a web-based resource such as eve-agents.com to search for agents, by empire, by high-sec region, by types of missions, whatever you want.

http://wiki.eveonline.com/en/wiki/Faction_Standing_Repair_Plan may be of interest