I've added a variable named @pattern
to store the search pattern string.
This calculates the number of matches by removing each instance of the pattern, determining the number of removed characters and then dividing the number of removed characters by the length of the search pattern.
DECLARE @pattern varchar(20) = 'Ted'
SELECT (Len(ColumnToSearch) - Len(Replace(ColumnToSearch, @pattern, ''))) / Len(@pattern)
AS Number_Of_Matches
FROM MyTable
If you need to do this calculation frequently, a function could easily be created based off of this.