I'm a Python newbie. I've read A Byte of Python, and read some texts from Learning Python. The problem is I can't write applications, solve problems, or do things with python.
How can I do these things? What examples should I start with and what books and references will help me learn these things?
That's normal. Start by taking examples you find interesting and modifying them. Take your time.
So, what kind task would you like to accomplish with your first program?
The best way to learn a new language is to work on some specific project. If Python is your first language you should probably start with something simple, like a command line calculator, or a script to count word frequencies in a text file. Code as much as you can, consulting reference materials such as books or sites like this when you have a Specific question. Then apply your skills to a more complex project.
If you are learning Python for a job or to accomplish some specific task then post some specific questions related to what you are trying to do and we will do our best to help. It's generally hard to give useful answers to vague questions.
Good luck!
That's like saying you learned how to use a hammer and nails but you can't build a house. There's learning how to use the tools and then there's learning about the actual design of how things fit together, and that mostly comes through practice, starting small with simple things and working your way up slowly to more complicated things.