Based only on these sensitivity and specificity values, what is the best decision method? If I have the following sensitivity and specificity values, what is the best decision we can say in this case?
sensitivity     specificity
-----------     -----------
  66.3             74.7
  87.2             65.9
  56.4             76.4
  79.5             94.3

Thanks.
 A: 
As Nick has already pointed out the answer depends on context. However, if you only had to judge based on the values of sensitivity and specificity values that you provided, then a good strategy is to plot the sensitivity on the y-axis and $(100\%-$ specificity$)$ on the x-axis and look for the highest leftmost point. This point would be the sensitivity and specificity pair that you might want to choose. But please remember that domain knowledge plays a huge impact on the final decision. Here is the R-code that does the work for you:
R> sens <- c(66.3, 87.2, 56.4, 79.5)
R> spec <- c(74.7, 65.9, 76.4, 94.3)
R> df <- data.frame(y=sens, x=(100-spec))
R> df
     y    x
1 66.3 25.3
2 87.2 34.1
3 56.4 23.6
4 79.5  5.7
R> df <- df[order(df$x), ]
R> df
     y    x
4 79.5  5.7
3 56.4 23.6
1 66.3 25.3
2 87.2 34.1  

R> plot(x = df$x, y = df$y, type = "b", 
     pch = 20, lty="solid", lwd = 2, 
     main = "Sensitiviy and (100-Specificity) Curve", 
     xlab = "100 - Specificity", ylab = "Sensitivity")

Therefore, you'd choose 79.5, 94.3 sensitivity and specificity pair. 
Basic Idea: High number for true positives and low number for false positives!
A: To make an optimal decision you need to know all relevant data about an individual (used to estimate the probability of an outcome), and the utility (cost, loss function) of making each decision.  Sensitivity and specificity do not provide this information.  That's why direct probability models such as the binary logistic model are so popular.  For example, if you estimated that the probability of a disease given age, sex, and symptoms is 0.1 and the "cost" of a false positive equaled the "cost" of a false negative, you would act as if the person does not have the disease.  Given other utilities you might make different decisions.  If the utilities are unknown, you give the best estimate of the probability of the outcome to the decision maker and let her incorporate her own unspoken utilities in making an optimum decision for her.
Besides the fact that cutoffs do not apply to individuals, only to groups, individual decision making does not utilize sensitivity and specificity.  For an individual we can compute $\textrm{Prob}(Y=1 | X=x)$; we don't care about $\textrm{Prob}(Y=1 | X>c)$, and an individual having $X=x$ would be quite puzzled if you gave her $\textrm{Prob}(X>c | \textrm{future unknown Y})$ when they already know $X=x$ so it is no longer a random variable.
Even when group decision making is needed, sensitivity and specificity can be bypassed.  For mass marketing, for example, you can rank order individuals by the estimated probability of buying the product, to create a lift curve.  This is then used to target the $k$ most likely buyers where $k$ is chosen to meet total program cost constraints.
