Understanding tides comes from understanding the relative positions of the moon and sun relative to the earth as this plays the biggest roll in how tides are generated and therefore affect diving conditions to a greater or lesser degree. The tidal swing; i.e. the maximum difference between the low and high tides, is either increased (when the Earth, moon and sun is in direct alignment - spring tides) or decreased when the moon is perpendicular to the sun's alignment with the Earth (neap tides). The reason neap tides have lower tidal swing is because the sun's gravitational force cancels out some of the lunar gravitational force to some degree (about half of the moon's "pull") when the moon is at 1st or 3rd quarter.
Since the Earth's orbit around the sun is elliptical the distance to the sun during the calendar year also affects the tides - so we see greater tidal swing during the winter (January in Northern hemisphere) when the Earth is closest to the sun (perihelion,) while the tides are less affected by the sun in summer months (July in Northern hemisphere) when the Earth is furthest from the sun (aphelion).
The same thing applies to the moon's slightly elliptical orbit around the Earth. There's generally a "higher" spring tide when the moon is closest to the Earth (perigree) and a "lower" spring tide when the moon is furthest from the Earth (apogee).
For a pretty nice explanation of the workings of tides check out:
NOAA National Ocean Service Education: Tides and Water Levels
So what you are looking for is when the tides are not swinging drastically - neap tides therefore generally offer better diving conditions than spring tides because there is normally less surge. Of course storm systems in the world's oceans also make for greater wave activity and this can also affect diving conditions through near-shore wave activity. Generally if the dive depth is less than half the wavelength of the waves you will experience swell and surge as the waves pass overhead. Diving to deeper than that should bring you past the wave bottom and you should be less affected by it.
Taking all this in consideration you'll want to dive during slack high tide, as most have already posted here, and also during neap tides for lower tidal swings.
For checking tides in US waters you could look at:
1-1 WaveCast
For checking storm systems check out:
1.
Weather Underground
2.
Wetsand's Tropical Center
3.
NOAA's Hurricane Center
For swell forecasts check out:
1.
Wetsand's Swell Forecast service
2.
Surfline
3.
Magic Seaweed
If you are really interested in learning a bit more about water conditions in the ocean I would recommend you start with Nathan Todd Cool's
Wavecast Guide to Surf Forecasting (see:
details here). He covers all the basics in pretty easy to understand language.
