Depending in what region you are crabbing will determine if you need to worry about tides or not. My best catches are normally around high tide. This is especially true when high tide is early in the morning. The combination of getting out on the water early, on a day when high tide is also early, usually produces the best catch.
Be sure to check your local laws to see when you are allowed to drop your first trap. There are restrictions in most states, for example some states will not allow you to start crabbing until an hour before, or an hour after sunrise. Other states will give specific start and end times.
Check your local tide chart. I like to start crabbing 2 hours before high tide if possible. Although I have caught crabs at all hours/tides, my best catch is normally when the water is moving. 2 hours before high tide all the way through 2 hours after high tide you'll find the water moving well and this is usually when you will bring in the most crabs.
With that being said, on some days I have also been rather productive during low tide. Again, the key is as long as the water is moving you will have your best chance of catching crabs. You will still catch crabs at anytime during the day but in my experience you will not catch as many if the water is not moving.