Adding integers in a single textbox (VB.NET)

If you are certain that every line in the text box is a number, you can do this:

Dim numbers = txtBox.Text.Split(vbCrLf).Select(Function(line) Double.Parse(line)).ToList()
Dim maximum = numbers.Max()
Dim minimum = numbers.Min()
Dim average = numbers.Average()

If you are not certain that every line is a number, then the statement that initializes numbers may throw an exception as it attempts to parse a non-number as a Double.

In that case, you could say

Dim lines = txtBox.Text.Split(vbCrLf)
Dim numbers = new List(of Double)
Dim unparseableLines = new List(of String)
For Each line in lines
    Try
        numbers.Add(Double.Parse(line))
    Catch ex as FormatException
        unparseableLines.Add(line)
    End Try
Next
' maybe report the contents of unparseable to the user?

The code as written uses the existing functionality in LINQ for finding Max, Min, and Average. If you want to implement Max or Min in a language that doesn't have these out of the box, you can do something like

Dim minimum = Integer.MaxValue
For Each number in numbers
    If number < minimum Then minimum = number
Next

As @Blackwood mentions, it's better to have a separate, canonical place you keep your data, and just use the text box to show these data to the user. That way you don't have to parse the numbers out of the text box to perform these operations on them; you'll just have the numbers directly from the process that created them.