It seems to me that you lack basic knowledge and understanding of arrays so you better of reading the Sun Tutorial
In general what you do is set the first element in the array to be the min (or max) and then iterate over the array comparing each element with the current minimum and set accordingly.
e.g.
int min = this.array[0];
for(int current = 1; current < array.length; current++){
min = (this.array[current] < min) ? array[current] : min;
}
In case you want to compare objects you would usually implement the Comparator interface which when used with Collections#sort can give you the min/max.
Although the first method works, depending on the number of elements your array has you are better of using a Sorting Algorithm to handle performance issues.