Assuming your foundation is poured, I believe what you want is hydralic cement. But w/o checking the bag myself, you need to do some reading. The reason I think this is right (and I could be wrong) is because you want the cement to expand and fill the crack.
I think you ought to wash the crack a little to get any loose debris out that's in there. Anything that's obviously loose, do remove. A quick swipe with a pressure washer or hose remove loose dirt. (Yes, you'll probably get some water in the basement so be prepared.) Depending on the size of the crack, you DO want to make it a little bigger if it's a hairline crack or slightly bigger. This way, you can work the cement into the crack and it will have some surface to hold on to. You'll need a hammer and a mason chisel. I don't know if you need to jam anything in there first to keep the cement from 'falling through' once you start sealing. Maybe some plumbers putty or something will work. Do dig down to the bottom of the crack, and if you find that chiseling at the lowest point is soft, keep chiseling. This condition would indicate deterioration behind the part of the foundation you CAN'T see. (I'd have to do this job twice!)
After that, with a clean crack and (perhaps) with something to keep the cement in place, away you go. I think this cement sets up real fast because it is expanding. Read the directions before you do anything. It may also be in order to use a cement sealer on the filled crack and the adjoining portion of the outside wall to help keep water out. All the home centers have this stuff. I wish I could help more but I hope I've raised enough questions.