Q:

When I change the EV compensation, how will that affect my aperture, shutter speed, or ISO?

Let say that we have the following values, as an example:
Shutter speed: 1/40
Aperture: 2
ISO: 1000

How can I get the EV number for this exposure, extract (or add) an EV value (0.33, 0.66 etc.) and calculate back the new shutter speed (or ISO) value?
In fact I want to calculate how the Exposure Compensation will affect my values.

A:

The Exposure value can be calculated with the given Aperture and shutter speed using the following formula:

(src: wikipedia)

where,
N: Aperture value
t: Shutter Speed
The above EV is for ISO 100 called as EV100. EV For subsequent ISO values is calulated with help of EV100 using the following formula:

where,
EV100: EV from the first formula
S    : required ISO value
The Exposure compensation works by adding or subtracting the required Exposure compensation value with the current EV to get the new EV.
This new EV can be reverse engineered with the above formulas to get the Aperture and Shutter speeds.
Applying the values you have given:
EV100 = 7.32  //At ISO 100
EV1000 = 7.32 + 3.32 = 10.64  //At ISO 1000

On applying Exposure Compensation of 0.33:
EV(new) = 10.62 +0.33 = 10.95

Now reverse engineer this value to get N and t accordingly.

A:

[I can neither comment nor vote (missing rep), but both the other answers with calculations are wrong]
Exposure Value (EV) is desribed as:

where N is the relative aperture, t the exposure time (shutter speed) and S the ISO speed.
An aperture N=f/1.0, a shutter speed of t=1s and an ISO speed of S=100 corresponds to EV=0. An EV of +1 means half the light, and EV of -1 means double the light of EV=0 will be exposed to the recording medium.
Source: Wikipedia
[Note: This seems counterintuitive, but a brighter scene requires a higher EV to be correctly exposed, while a darker scene requires a smaller EV to be correctly exposed. ] 

Given your numbers your total EV will be:

Now exposure compensation works the opposite as EV. A positive exposure compensation (brighten up picture) will decrease EV, a negative exposure compensation (darken picture) will increase EV. So you need to subtract your compensation from the EV. 
Source: Wikipedia
Applying your exposure compensation of +0.33:
EV = 4 - (+0.33) = 3.66

You can reverse engineer this value in order to get either a new N, t or S. For example applying an exposure compensation of +0.33 (brighten up picture) will have the same effect as increasing your exposure time to t=1/32.

