Question: I have replaced three flats on my new bike and found each time a tear or hole at the base of the air valve. What can cause this.

Answer: 
1. As Kibbee suggests, the wrong size valve.
2. A badly-formed valve hole in the rim. It's not that unusual to find that there is a "lip" of metal at the hole that will cut into the tube. This requires a bit of filing with a small round file to correct.
3. Running the tire flat or with very low pressure. As an under-inflated tire rolls on the ground it tends to "walk" along the rim, tugging on the valve stem.
4. Poor tube installation technique. Most importantly, inflate the tube slightly before installing -- just enough that it rounds out (though it should still be limp).
The most likely cause is using a presto valve is a rim that's drilled for Schrader. Make sure you're using the correct tube for your rims. You can get a grommet to fill the hole if you want to use presto tubes on rims that are drilled for Schrader. 

It might also be because the pressure was too low. This can cause the tire to be able to move around inside the tire, and would mostly occur during braking.

Check on the valve hole to make sure there aren't any rough edges, and file them down (only lightly, be careful) if the hole has any sharp edges.