Method/Unit for measuring activity in specific frequency band for EEG This may be more of a signal processing question but I'm looking to measure and compare activity in different frequency bands for each sensor. Unfortunately, all papers I've looked at simply refer to "alpha activity" without specifying how this was calculated. 

Is there any standard method or "best practice" to measure the level of activity? Is it simply the average energy in the band (sum of the square of the absolute of the signal?) 

Any help with this would be appreciated.
How you analyse your data depends a bit on how you did your time-frequency decomposition.

If you're using a fast Fourier transform, you will likely cut out the temporal window of interest prior to analysis, and your power estimate will be a single value (per subject and/or condition) within this time window. For example, alpha wave desynchronisation is likely to kick in something like 100 ms after the onset of a tone, and you might be interested in its power between then and 300 ms. This is based on theory and literature, there is no single answer. But if you do cut out a time window in advance like this, make sure that the time window of interest is an exact multiple of the size of the cycle you are looking at! (e.g. a multiple of 1/10th of a second for 10 Hz.) Otherwise you might get some nasty artifacts.

What you will then end up with is one data point per subject and condition, per EEG sensor. Some people pre-select a group of sensors based on the literature, and look at average power across these sensors. In that case you can use any of the standard parametric statistics to test your hypotheses.

Alternatively, you might adopt a sliding time window or similar approach (see here), where you get an estimation of how power develops over time (per sensor and frequency band). In that case your data space is larger, and the usual way to constrain it is to use cluster-based permutation tests which are nonparametric. This will give you back clusters of significant differences across time and/or sensors (this means groups of successive time points or sensors near each other that show an experimental effect). Again, whether you want to average across sensors is a theoretical question. You can also decide to average across time using this approach, and to end up with a single data point per subject/condition as above. This approach is not particularly temporally precise - the data will be a bit smeared across time - but it gives you a better overview of what is going on in the brain and in which frequency bands the interesting effects might lie.

As for the unit, I prefer to convert raw power to decibel, because the scale is symmetric around zero and comparable across experiments. So, 10*log10 of the power in your signal. If you're using a baseline, make it an absolute baseline (it's equivalent to a relative baseline for raw power, which is the standard).