College Student needs advice

Hello all! I have previously owned two family cats (indoor). Recently, my roommate and I have noticed two cats live by our house. We feed them at night, however we are starting to have a problem of Raccoons and Skunks trying to eat their food as well. One of the cats has a red eye and we think it is pink eye, so I want to get it to a vet. One of the cats lets us get pretty close to it while it is eating, but I don't try and touch it because I'm afraid it will bite me and I haven't had it treated at the vet yet. What advice can you give me about getting a feral cat to feel comfortable enough to let you pet it? I want it to feel comfortable enough with me that I can pick it up and take it to the vet that luckily is only one minute away from my house! I read online that you should try feeding it from a spoon then trying to pet it once it is close to you, but I don't want the cat to freak out. Please help! 

Going through same situation now. Been feeding a female for over a year. At first she wouldnt come anywhere near me and ate after i left. Over time she came closer to me, but only during feeding time. Just recently i was able to grab her by her scruff of the neck(wearing gloves and a long sleeve shirt of course)and with her fighting put her in a carrier and off to the vet i went. You will most likely have to trap them in a  trap that triggers or drop trap. I like the drop trap, cause its very wide and you can be right there to pull the string and see what comes in there to feed.She was trap savy on both kinds thats why i took the chance to grab her.  You can contact your vet or your local shelter for the use of a trap.