As I understand it, the railroads only answer to the Federal
Government. Therefore, if a railroad wanted to add another track
within their existing right-of-way, would they have to go through the
NEPA process? If yes, would they also have to go through the State and
local processes?

Or maybe the simple question is, can a railroad construct with
right-of-way that they already have? If not, what permits do they have
to obtain? A summary of some actual cases would be helpful as well.

Hello Powhatan.  Railroads do indeed have to comply with NEPA
requirements to construct rail lines other than "minor rail
additions."  However, they do not have to comply with any state or
local requirements, as Federal law preempts state law in this field.

The Federal Railroad Administration has numerous procedures for
complying with NEPA:
http://www.fra.dot.gov/us/content/166
However, some activities are ?categorically excluded? from the
requirement of compliance, including:
?Minor rail line additions including construction of side tracks,
passing tracks, crossovers, short connections between existing rail
lines, and new tracks within existing rail yards provided that such
additions are not inconsistent with existing zoning, do not involve
acquisition of a significant amount of right of way, and do not
significantly alter the traffic density characteristics of the
existing rail lines or rail facilities?

For whatever interest it holds, here is a firm that has done NEPA
compliance work for railroad construction:
http://www.icfconsulting.com/Markets/Environment/enviro4.asp#2
?ICF Consulting has prepared or reviewed EISs and EAs, on both the
government side (STB) and the applicant side, for several important
railroad construction projects, mergers, acquisitions, and
privatization activities. These include the construction of the
Bayport Loop in Houston, the merger of Burlington Northern and Santa
Fe (BNSF), the Canadian National (CN) acquisition of Illinois Central,
the CSX and Norfolk Southern acquisition of Conrail, the proposed
BNSF-CN merger, and the Long Island Rail Road privatization of freight
operations.?

Here is a letter threatening suit for railroad harassment of birds:
http://www.wildcalifornia.org/pages/page-68

A railroad president testifies before Congress about the obstacles
that NEPA compliance poses:
http://www.house.gov/transportation/rail/05-22-01/schieffer.html

So it?s pretty clear that the NEPA applies to the railroads.  You then
ask, do they also have to go through the State and local process?  And
the answer to that depends on the question of Federal pre-emption.

Federal law, and the actions of Federal administrative bodies, may
pre-empt State law under certain circumstances.  ?Specifically,
federal law may preempt state law (1) when Congress has expressly or
implicitly preempted state law in the language or structure of a
federal statute, Jones v. Rath Packing Co., 430 U.S. 519, 525 (1977);
(2) when Congress has, despite the absence of express preemptive
language, exhibited an intention to occupy an entire field of
regulation by enacting a comprehensive regulatory scheme, Fidelity
Fed. Sav. & Loan Ass'n v. De la Cuesta, 458 U.S. 141, 153 (1982); or
(3) when compliance with federal and state law is impossible because
the two conflict or state law poses an obstacle to the achievement of
the objective of federal law, Pacific Gas & Elec. Co. v. Energy
Resources Conservation & Development Comm'n, 461 U.S. 190, 204 (1983).
The actions of a federal administrative agency may also preempt state
law if such administrative action is within the agency's
congressionally delegated authority. Louisiana Pub. Service Comm'n v.
Federal Communications Comm'n, 476 U.S. 355 (1986).?
http://www.cslib.org/attygenl/opinions/1995/1995-029.htm

Federal regulation of the railroads has indeed been found to pre-empt
State and local environmental regulations.

In City Of Auburn v. US Government (9th Cir. 1998) 154 F.3d 1025,
cert. denied, 527 U.S. 1022 (1999), ?the City of Auburn challenge[d]
the STB?s [Surface Transportation Board?s] finding of federal
preemption of state and local environmental review laws in approval of
the reopening of the Stampede Pass line, and object[ed] to the lack of
a full Environmental Impact Statement.?  The Ninth Circuit Court of
Appeals upheld Federal pre-emption and held that satisfaction of
Federal environmental review was sufficient.
http://caselaw.lp.findlaw.com/cgi-bin/getcase.pl?court=9th&navby=case&no=9671051o

See also Friberg v. Kansas City S. Ry. Co., (5th Cir. 2001) 267 F.3d
439; and Railroad Ventures, Inc. v. Surface Transp. Bd. (6th Cir.
2002) 299 F.3d 523.

I hope this has been helpful and answered your question sufficiently. 
If I can provide any further assistance, please ask for clarification
before rating this answer.  Thanks!