Christy,
The amount of water to provide your tree is dependent on the size of your containers and the growing medium you use. I use a very fast draining growing mix in Houston so I can water every afternoon during the hot summer months to cool down the root zone. I usually provide about .75-1 gallon of water per 3.5 gallon nursery container per day, and about 1.5-2 gallons per 7-15 gallon containers. The 30 gallon containers get about 6 gallons every other day.
Before it gets too hot or as the summer starts to wind down, I let the trees go until the leaves start to wilt during the peak heat of the day. Then I water at the same rates as above. Basically, there is only a small amount of water that escapes from the bottom of the containers. Depending on how fast your mix is, your watering schedule will vary.
Some things to keep in mind: Drip irrigators are not so efficient at watering. The water ends up forming a canal through your growing mix and does not spread through out the container. Instead of a drip, you might want to consider a micro-sprinkler. I had looked at the Spot Spitters in the past and they seemed pretty cool. I have since seen many nurseries in the area use them.
I fertilize with every watering. I use a weak fertilizer solution that is siphoned into the hose. The amount given to each plant is somewhat regulated by the size of the container. Every so often I flush each container with regular tap water, then follow up later in the day or the next day with the fertilizer regiment. You can find various systems which hook up to your system to provide nutrients if you wish.
Generally, the irrigation system manufacture will provide information regarding flow rates of their emitters. You should be able to very easily calculate the number of emitters needed in each container (e.g. 1 emitter in a 1 gallon container, 3 emitters in a 5 gallon container, etc.), then adjust the time to provide the proper amount of water. One other precaution on using automated systems during the heat of summer (especially those with black tubing) is the first bit of water coming through may be hot (140 degrees F +) which could damage the roots in the containers. You may want to find a way to flush the line with cool water before the containers are watered.
~james