k-fold cross-validation is implemented by taking the set of n observations and randomly splitting into k non-overlapping groups. Each of these groups acts as a validation set and the remainder as a training set. The test error is estimated by averaging the k resulting MSE estimates.
i. The validation set approach is conceptually simple and easily implemented as you are simply partitioning the existing training data into two sets. However, there are two drawbacks: (1.) the estimate of the test error rate can be highly variable depending on which observations are included in the training and validation sets. (2.) the validation set error rate may tend to overestimate the test error rate for the model fit on the entire data set.
ii. LOOCV is a special case of k-fold cross-validation with k = n. Thus, LOOCV is the most computationally intense method since the model must be fit n times. Also, LOOCV has higher variance, but lower bias, than k-fold CV.