I'm guessing if it didn't come with all the hardware it also didn't come with a manual. Look up the specific model number online and download the manual which should tell you exactly what screws will be the right fit.
Remember that 'drop-side' cribs are no longer considered safe and have all been recalled - if that's the kind you bought you'll want to check online for tutorials on how to anchor the drop side so it's no longer moveable.
The safety of your baby is worth a whole lot more than the cost of a piece of furniture that you know for sure is safe and fully functional. You might want to consider buying new if you aren't absolutely positive you can replace the missing parts - I personally wouldn't have bought something incomplete like that from a yard sale. I'd be too worried about the possible consequences of prior damage during use, moving, storage... all of which I would have no information on after purchasing it from strangers.
Yeah find the size and what type if screws and go to lowes or home depot.
Find out what sizes you need and go to any hardware store! :)