<p>I'm looking for a simple, easy to understand algorithm to alphabetically sort an array of characters in C.</p>

Easy?  Do a bubble sort.
This is java and int rather than char, but you can easily adapt it...
```
```
int[] bubble(int a[])
    {
    for (int i = a.length; --i>=0; )
        {
        for (int j = 0; j<i; j++)
            {
            if (a[j] > a[j+1])
                {
                int T = a[j];
                a[j] = a[j+1];
                a[j+1] = T;
                }
            }
        }
    return(a);
    }
```
```