1) Wash your hands well, with soap and water.

2) Rinse your hands clean of the soap.

3) Cup your hands together to hold cool water from a flowing tap.

4) Put your eye in the cupped water, open and close your eye repeatedly.

5) Flush out your eye a few more times this way.

6) This should flush out the bacteria from the dog, before an infection takes hold. You could also have an allergic reaction to dog-proteins (like my GF does), so flushing out your eye this way is a good idea.

7) As an added precaution, in many places in the world you can get antibiotic eye drops from behind the counter, without prescription. Just ask the pharmacist. You can give yourself a course of 10 days (twice a day?) of the drops. But, if you feel a reaction to the eye drops, then stop (of course), and see an eye doctor.

I would guess the antibiotic eye drops are most likely not necessary, but some people are prone to eye infections, so if you are one of them...