I'm sorry to hear about your dog‘s eye. If attempting to treat at home you want to be very careful first of all that the eye continually looks better through treatment, and no signs of rubbing at it, reddening worse, or cloudiness appear in the eye.
You should rinse the eye extremely well with sterile saline, like that found in regular contact lens solution, and do not let the tip of the container touch the eye. Make sure it is not the disinfecting/storing type of contact lens solution, just the normal saline/ NaCl. You can wipe around the eye with the saline soaked on a soft cotton ball or gauze, but don't use anything harsh like paper towels. Rinse, rinse, rinse! You can't over do it! It may be difficult to try to keep the eye open and do this, but it's pertinent!
Once rinsed, if you see any redness or discharge appears in the next day or two, an infection is likely starting and you can also find an ophthalmic antibiotic ointment at a pharmacy: like terramycin, triple antibiotic (neo/poly/bac), etc. Ask the sales people if you need help, but it does need to be safe for the eye, not a topical one for skin. After rinsing the eye, apply the ointment 3 times a day (every 8 hrs) for 10 to 14 days.
This may become conjunctivitis, but could also be a scratch or ulcer forming from whatever got in there, and if not starting to clear up in a couple of days, you'll need a vet to check it.
Best of luck, and let me know if I can help further.