1. Do I have a correct understanding of what attribution is? If not, describe why I am wrong.
In the GPL family of licenses (and in many other licenses), attribution comes in the form of a copyright notice. You may also provide attribution in other forms, but this is a courtesy not required by the license.
2. What part in the LGPL 2.1 license text states the requirement of the attribution?
There are two attribution requirements in LGPL 2.1. The first is in section 1, which applies to any distribution of the source code (including modified code and mandatory source distribution alongside machine code):
[you must] conspicuously and appropriately publish on each copy an appropriate copyright notice and disclaimer of warranty
Simple enough: in the source code that you distribute, include correct copyright information and don't remove messages that indicate the licensing status of particular files under the LGPL. (e.g., the headers that start with, "This library is free software; you can redistribute it...") This requirement does not affect non-source binary files you distribute; those will be covered in the next requirement.
The second requirement is in section 6. It applies to the distribution of a larger work that includes a linked LGPL library:
You must give prominent notice with each copy of the work that the Library is used in it and that the Library and its use are covered by this License. You must supply a copy of this License. If the work during execution displays copyright notices, you must include the copyright notice for the Library among them, as well as a reference directing the user to the copy of this License.
So, you must "give prominent notice" that he library is used by your software, and display copyright notices for the library, if your software displays any copyright notices.
3. How do I do the attribution to the 3rd party dependency specifically?
You may do so in any reasonable way. The FSF (the author of the LGPL) says of this requirement:
Some common and acceptable ways that "prominent notice" is done is by clearly giving a notice in the user manual that accompanies the software, by stating a notice in an "About" box in a GUI program, or by printing a notice on the screen at System startup. In general, much flexibility is available for giving this "prominent notice".
An example for the first part (e.g., that you might include in a manual or About screen) could look like
This program uses the Foobar Library, which is licensed under the GNU Lesser General Public Library, version 2.1.
If you show copyright notices in your program, then you must also include a copyright notice and pointer to the LGPL:
This software uses the Foobar Library.
Copyright 2016 Jane Doe
The Foobar Library is licensed under the GNU Lesser General Public Library, version 2.1. You can find a copy of this license at https://www.gnu.org/licenses/lgpl-2.1.en.html