We use TestComplete exstensivly, It is such a powerfull and complex tool. There is no way i can help you learn this tool. But here is a list of what you need to do to learn
all of the power comes from what you can do through scripting
2. Learn Data-driven automated Testing.
if you can incorporate this into your testing, your going to impress somebody with the power of automated testing
3. THey help section of TestComplete is very thorough
4. visit www.sqaforums.com
they have a TestComplete Section. Verry active with great archive. much more info youll get from there then here