After logging in, you use the Navyfield Fleet Mission tab, and there are 4 options:
Fortune Wheel: requires 30 KPscore per try and has a modest chance for 1000 credit/point and very low chance of a wide range of other prizes. Click on the first of the three colored buttons (the red one) at the top left to pay for tries.
Gold Egg Lottery: requires 30 KPscore per try and has a low chance of getting BB/CV/SS Starter Pack or Hero Sailor pack. Click on the first of the 3 buttons under the eggs (the yellow under the 4th egg) to load tries.
Jewelry Box Lottery: 30 KPscore per try and has a low chance of Super Elite sailors (Torpedo, Restore, Fighter, or Bomber).
Supply Box Lottery: 60 KPscore to play, with range of prizes including sailor items and higher chase items, but all at infinitesimally low rates:
-Sailor has assorted sailors (super elite or better) as top prizes, with the best being NF-X
-BB/CV6.5 has the 6.5s as top prizes, with 1 week prem and sailor items at mid
-BB/CV7 is as above, but gives you a 7 if you're powerball lottery level lucky
I should note that in all cases, the overwhelming majority of tries will just get back 10 of the KPscore you just used. Supply box has the lowest rate (by far) of anything else - less than 1% for anything useful, while the Fortune Wheel has the highest - about 20-30% chance of getting 1000 credits or points based on my experience.