Running matplotlib in tkinter
Have a look at the examples for embedding plots in a tk GUI, it should be enough to get you started in the right direction.
user_interfaces example code: embedding_in_tk.py
user_interfaces example code: embedding_in_tk2.py
As for removing the toolbar, it's a case of not adding it when you are embedding plots in a GUI.
If you are using matplotlib.pyplot the toolbar will be created automatically for every figure. If you are writing your own user interface code, you can add the toolbar as a widget.