Wildcards worked for me when the string I was searching for could be entered manually. However, I wanted to store this string in another cell and refer to it. I couldn't figure out how to do this with wildcards so I ended up doing the following:
A1 is the cell containing my search string.
B and C are the columns within which I want to count the number of instances of A1, including within strings:
I had similar problem however the various count solutions still wouldn't work even with wildcards of "*"& etc..... My problem was caused by &nbsb (hidden spaces) which is hidden in the background when copying eg data from a webpage. This prevents the find from working properly. Use: