I'd suggest to start with this:
Comparing Strings in .NET | Microsoft Docs[
^]
If you want to ignore case, check this:
String.Equals Method (System) | Microsoft Docs[
^]
Dim node2find = Me.TreeView1.Nodes.Cast(Of TreeNode)() _
.Where(Function(n) n.Text.Equals(TextBox3.Text, StringComparison.InvariantCultureIgnoreCase)) _
.ToList()
Above code will return a list of nodes which text equals to
TextBox3.Text
ignoring case.
[EDIT]
In case you want to compare a part of text, you need to use of of the following string functions:
StartsWith
Contains
EndsWith
Please, follow the first link (on the top of my answer).