A group is a collection of triangles that have been assigned a common name. A group can be part of a mesh, or composed of multiple meshes. Groups may have materials applied to them.
A group can be created using the Groups Window or the Group Properties panel. To create a group from the Groups Window click the "New" button. To create a group from the Group Properties, select one or more faces and then select <New> from the Group drop-down menu.
To apply a texture map to a group, you must first create a material. You can do this using the Materials Window. All faces in a group share the same material. A material may be used by more than one group.
To change the way the texture is mapped onto the faces of the group you will need to move the Texture Coordinates Window. Sometimes using a Texture Projection gives you a good starting point for texture coordinate assignment.