I've attached a file that reviews research on vigilance tasks in the human-factors end of the psychological spectrum. It includes many interesting references that you might follow up for applicable measures/tasks for studying attention.
Can you be more specific? Do you want objective or subjective data? First thing coming in my mind is Eye Tracking, but it all depends from the experimental design!
Sir Damian G Kelty-Stephen , thank you so much for this reference sir. I'll sure read through this. May i ask though if this material is in the context of pure psychology or interdisciplinary like HCI?
Hello Sir Davide Salanitri. Yes sir! That is one of the definite tools that i have looked into! Eyetracking and also a BCI-EEG that reads Beta Waves. I am more concerned though which is a better tool to use and how to rightly quantify measurement of Attention at certain episode of learning.
It's interdisciplinary like HCI. I would hope that it is what pure psychology aim towards explaining, but it does focus on more applied aspects.
Here's another article that might link the review of vigilance tasks up with the broader cognitive/neuroscientific interest in attention: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2865224/
There is a new eyetracking method showing up here and there for measuring effects of emotions, mainly pupilometry. Additionally, to deal with obvious problem of luminence, one compares variation in pupil size between eyes. This is not my field of expertise at the moment, but people I talked to are highly optimistic about this method.
In sports research, for example, in investigating the level of sports fit of an individual, there is a test that measures up to 20 reaction times (consecutively and with breaks of varying duration). From their duration curve analysis may result his own attention status. If the time duration curve decreases it may be concluded a good sport form or fit, (i.e. a good level of attention) and vice versa. The investigation requires a sensitive electronic timer (1/1000 seconds). The trigger stimuli can be: auditory, visual or haptic. The experimental procedure can be single or dual-task as was saying by Mr. Adam Reeves. Best regards, Nicolae.
It really depends on your specific question. You may want to measure attentional bias for which you can use task like spatial cuing task, dot-probe ad etc or you may want to measure attentional control or something else. Taking keywords into account you can also use eye-tracking for research on attention.
As alluded to by Abi above, you would need to be more specific on your definition of "attention", as it has become such a broad term.
Marvin Chunn has an excellent review of this problem in Annual Reviews of Psychology called "A taxonomy of external and internal attention" which can be found in the attached link. It gives an overview of the different types of attention, and you will be able to find references regarding the type of attention you are interested in measuring.