Well, first you have to think about why you kept taking the temperature of the water. As I'm sure you've discovered, the temperature of the water went up when the wood was burning. Now why would the temperature go up? The temperature went up because it absorbed energy from the burning wood. Calories are a measurement of energy. If you know how much the temperature changed and you know what the specific heat of water is, you'll know how much energy it absorbed which would then be equal to the energy given off by the wood. (Well, equal enough for your purposes. In reality, it's not 100% equal due to various losses). Also, specific heat is a measurement of how much energy is required to change a specific mass of a substance one degree Kelvin. (A change of 1 degree Kelvin is equal to a change of 1 degree Celcius. The units of specific heat are 'Energy/mass*Kelvin'. So a specific heat of 2.06 J/g*K means that for every 2.06 joules, one gram of the substance will go up in temperature one degree Kelvin).
In order to calculate the calories, you need to find the specific heat of water and the temperature change you observed. You'll then need to do some basic math and make sure the units match up. It shouldn't be too difficult.