Before I answer the question about placing the templates on your fabric, it is a good idea to understand about the grain of fabric. As you see in the picture, the selvedges are the woven edges of the fabric and define the straight grain.
Perpendicular to the straight grain is the cross grain of the fabric. The bias runs diagonally across the fabric.
Now to the templates. If you are cutting squares or rectangles, you will want to place the straight sides of the templates so they match up with the straight grain and cross grain.

When you cut triangles, your template should be placed so the straight sides of the triangle that form the 90 degree angle (the square angle) match the straight grain and cross grain. That means that the long hypotenuse of the triangle will be placed on the bias.
In the picture on the right, the strip has been cut along the cross grain of the fabric - from selvedge to selvedge.
Hope that helps!
Happy Quilting!
Penny Halgren
www.How-to-Quilt.com
www.TheQuiltingCoach.com