The amount often depends on the missions you do chap, if you are just doing simple trading missions, maybe try some kill or collect missions, I found the quickest way for me to go for was assassination missions that made them happy quicker and allied with the Feds and the local minor fed faction that had issued the missions. Also move around the local stations more if you just want Fed rep to get to a petty officer or above with the main fed faction, or stay with the locals if you want to help that minor fed faction to get allied with that station or system.
You do get slow reputation upgrades for just trading with a fed system and being friendly and not breaking any laws too chap. My rep went up first because I was just trading a lot with the Feds, then later I chose to go for the kill missions to get my rank up a bit with them so I had the rank to buy a Fed Dropship when I had the credits.
Once you get allied you get scanned less if you do not change ships often and it's a little easier to smuggle into the big stations then chap, but still somewhat risky too..