"I'm just trying to understand the concept of anatta better here. Buddhism tells me there is the concept of no-self (anatta) [...] (correct me if I'm wrong)."
I'll quote @suminda's sucint description of anatta here:
Saying there is no self is a bit of a mistranslation or abbreviated translation. A better translation would be "there is nothing you can take as me, mine or self, which is permanent, non changing and persistent;"
When the suttas (and, consequently, the Buddha) speak of anatta, often they understand atta/self to be:
- a fixed/unchanging essence
- an eternal essence
- an essence that is never dukkha
- an essence that is under your complete control
In summary, Buddha's doctrine teaches how to observe every single aspect of yourself raising and ceasing, and under which conditions they do so. At the end, one comes to the conclusion that every aspect of what constitutes "him/her self" is conditioned: raises and ceases under certain conditions. Therefore, in summary, one concludes nothing possessing all the features above can be found.
As illustration, Nagasena and King Milinda debate:
[...] "How then did you come on foot, or on a mount?"
"I did not come, Sir, on foot, but on a chariot."
"If you have come on a chariot, then please explain to me what a chariot is. Is the pole the chariot?"
"No, Reverend Sir!"
"Is then the axle the chariot?" No.."Is it then the wheels, or the framework, of the flag-staff, or the yoke, or the reins, or the goad-stick?"..."Then is it the combination of poke, axle, wheels, framework, flag-staff, yoke, reins, and goad which is the "chariot"?"... "Then, is this "chariot" outside the combination of poke, axle, wheels, framework, flag-staff, yoke, reins and goad?"
"No, Reverend Sir!"
"Then, ask as I may, I can discover no chariot at all. This "chariot" is just a mere sound. But what is the real chariot? Your Majesty has told a lie, has spoken a falsehood! There is really no chariot!
-- Milinda Panha
Above, Nagasena is alluding to an "essence of the chariot", and showing there isn't one, as an analogy. It's said "illusion" because it's easy to believe something inside is unchanging, etc. Naturally, we say "you" and "I" and "myself", as this is useful and understandable in the day-to-day. And I'm pretty sure I'm writing this right now (or, to be more precise, the experience of writing this text right now is been felt). This is no illusion.
"But psychology tells me on the other hand, that there exists something called Volition or Will."
Buddhism psychology also refers to volition, calling it cetanā. In general, it is grouped in the saṅkhāra-khandha.
"So you see, there needs to be an individual or self who needs to take the decision or make the will, so to speak."
It's not necessarily true that an individual (unchanging, etc) self needs to be. It is quite possible for a composition of ephemeral "things" (of which "volition" can be a part of, as well as a nervous system, and so on) connected to each other, to interact and, in this interaction, things happen -- and complex behavior appear. (Biologists and computer scientists are no strangers to systems "that have no core", composed by simple parts, but exhibit complex behavior).
[Edit] "As a practical example, I decide to lift my hand right now, and lo and behold! my hand is lifted instantly" In the comments: "what was the decision to lift the arm right now conditioned or caused by?"
I understand that our (unenlightened) volitions, individually (like writing this text), are caused by delusions, desires and aversions -- and perhaps "habits" which is also a placeholder for subtler or deeper kinds of desires and aversions. With the cessation of the specific desires/aversions (by their consummation or extinguished otherwise) there is the cessation of the specific volition. In the Buddha's words:
"Monks, these three are causes for the origination of actions. Which three? Greed is a cause for the origination of actions. Aversion is a cause for the origination of actions. Delusion is a cause for the origination of actions.
-- Nidana Sutta: Causes AN 3.33
The above actions are said to "generate kamma fruits". That is, they are seeds that are capable of germinate, to come to fruition.
"What about an Arahant?", you ask. As far as the texts go, an Arahant still possesses the 5 aggregates, and naturally still perform actions. Supposedly, these are directed by volitions. However, it is said such actions are not "tainted" and have a distinct quality due to the "cool down" of his deepest clinging and cravings. There is no desire for "having" or "becoming". In the same sutta above, the Buddha continues:
"Now, these three are [further] causes for the origination of actions. Which three? Non-greed is a cause for the origination of actions. Non-aversion is a cause for the origination of actions. Non-delusion is a cause for the origination of actions.
"Any action performed with non-greed — born of non-greed, caused by non-greed, originating from non-greed: When greed is gone, that action is thus abandoned, its root destroyed, made like a palmyra stump, deprived of the conditions of development, not destined for future arising.
Finally, in a higher perspective, the general form of the paṭiccasamuppāda formula has kamma volition (or, more specifically, saṅkhāra*) conditioned by ignorance -- that is, with the cessation of ignorance, there is the cessation of saṅkhāra. I understand this is not about a specific volition like raising an arm, but all volitions [whose kamma may come to fruition].
(*)Note this saṅkhāra is not considered to be the same as saṅkhāra-khanda mentioned above
"So, who is this decision-maker or will-maker? You say there is no self?"
One way of seeing it is that there is decision as a product of interacting processes. I guess one is free to call volition the decision-maker on his own. But, according to Buddhism, regarding that volition/"decision-maker" possessing the features in the list above is a faulty view, and under careful scrutiny, it should show it's true nature (perhaps just as atoms, under careful scrutiny, were shown to be not atomic at all).