How would you get the index of the lowest value in an int array?

Since you mention MoreLinq, how about:

int[] array = ..

// Will throw if the array is empty.
// If there are duplicate minimum values, the one with the smaller
// index will be chosen.
int minIndex = array.AsSmartEnumerable()
                    .MinBy(entry => entry.Value)
                    .Index;

Another alternative:

// Will throw if the array is empty.
// Requires two passes over the array. 
int minIndex = Array.IndexOf(array, array.Min());

You could of course write your own extension-method:

// Returns last index of the value that is the minimum.
public static int IndexOfMin(this IEnumerable<int> source)
{
   if(source == null)
     throw new ArgumentNullException("source");

   int minValue = int.MaxValue;
   int minIndex = -1;
   int index = -1;

   foreach(int num in source)
   {
      index++;

      if(num <= minValue)
      {
         minValue = num;
         minIndex = index;
      }
   }

   if(index == -1)
     throw new InvalidOperationException("Sequence was empty");

   return minIndex;
}

With some effort, you can generalize this to any type by accepting an IComparer<T>, defaulting to Comparer<T>.Default.

LINQ probably isn't the best solution for this problem, but here's another variation that is O(n). It doesn't sort and only traverses the array once.

var arr = new int[] { 3, 1, 0, 5 };
int pos = Enumerable.Range(0, arr.Length)
    .Aggregate((a, b) => (arr[a] < arr[b]) ? a : b); // returns 2

Update: Answering the original question directly, this is how I would do it:

var arr = new int[] { 3, 1, 0, 5 };
int pos = 0;
for (int i = 0; i < arr.Length; i++)
{
    if (arr[i] < arr[pos]) { pos = i; }
}
// pos == 2

No, it doesn't use LINQ. Yes, it is more than one line. But it is really simple and really fast. Make it into a tiny little method and call it from anywhere on a single line: pos = FindMinIndex(arr);