It depends on what "kind" of dirt is in your eye, however I find that usually rinsing it with water works well.  The best way is to lean into the sink, cup your hand, run some water into it and put the water up to your eye with your eye open. Some people may not be able to do this, however I have been wearing contacts for 12 years so I am ok with things going into my eye lol.  When I'm wearing contacts and get dirt in my eye, but can't take them out, I use Visine for contacts, it works REALLY well!