d4 d5 e3 Nf6 c4

Is Nf6 simply a bad move for black?  It seems that all moves lead to a bad position for black.  Nf6 could be replaced with other moves, but I do not know how to deal with the c4 pawn.  Taking it lets white develop his bishop while ignoring it leads to white c5, which I find difficult to deal with.

Any commentary is welcome.

There's your problem. You think white playing c5 is a good thing, but it's not. For example:

1. d4 d5 2. c4 e6 3. c5? can be simply met with 3... b6 4. b4 a5 when white's queenside expansion is toast. The move c5 by white is just a bad move all around at this early a juncture:

1. It ignore's development
2. White almost always has a hard time maintaining the space
3. White's loses a lot of influence in the center (such as opening a file via pawn capture)
4. Black gains two nice break moves ...e5 and ...b6
5. c5 by white gains space at the cost of time, but this added space rarely does anything for white. Black can easily develop despite it. 

edit: Also... you do know that white can play c4 on move 2, right? It does not need the prep move 2. e3.

After 1.d4 d5 2e3 not very inspiring 2...Nf6  3c4 a wide range of moves are fine for black. 3...pxp leads to a Queens Gambit accepted position, a main-line position probably more than white deserves. 3...c6 is a slav position. 3...g6 a not particularly challenging line of Grunfeld. 3...e6 is an old fashioned form of Queens Gambit declined. Probably c5 is perfectly ok too.

Almost any "sensible" move equalizes for White.  2.e3 is utter sh*t.  Here's the problem:

1) Compared to 2.c4, it does nothing to pressure d5.  Black has a free hand.

2) Compared to 2.Nf3, it does nothing to control a second central square, namely e5

3) Compared to lines like the Queen's Gambit, Trompowsky, Torre, London, etc, it hems in the Dark-Squared Bishop.  While hemming in a Bishop is ok on Defense, why would the attacker want to block his own pieces that early?

4) Compared to the Nimzo-Indian Rubinstein Variation (1.d4 Nf6 2.c4 e6 3.Nc3 Bb4 4.e3), there White's Bishop is behind the pawn chain, Black has committed to nothing yet.  After 1.d4 Nf6 2.e3 or 1.d4 d5 2.e3, Black can play any defensive structure where White would normally want his pawn on e4 instead of e3 (i.e. King's Indian/Grunfeld structures by fianchettoing the Kingside).  In the Nimzo, Black has committed his Bishop to b4 instead of e7 (he can retreat, but costs him a tempo), and in many cases, White waits for a3 until Black is virtually forced to take on c3, so White solidifies until he can get caught up in development, then put his bishop pair to work.

So now you might ask "So why is the Stonewall Attack so bad when the Dutch Stonewall is played all the time?"  It all has to do with commitment.  As a former Bird's Opening player, you could not go into the game pre-meditating the Stonewall Attack and succeed.  Many times, the Classical, Antoshin, or others were necessary.  The same thing goes for the Dutch.  You can't play a Stonewall and expect to succeed if White is still able to get his Bishops to f4 and d3 without harm to the pawn structure.  Hence why lines like 1.d4 f5 2.c4 Nf6 3.Nc3 e6 4.Nf3 d5?? are so bad (4...Bb4 is the correct move here, with an improved Nimzo) due to 5.Bf4!, 6.e3!, and 7.Bd3!.

After 1.d4 d5, Black has committed to very little, and so to play a move like 2.e3 here is just completely giving up all advantage you ever get for playing White.  A more productive move like 2.c4 or 2.Nf3 or even 2.Bg5 (against 1...Nf6) is far superior to 2.e3?

This past Wednesday, I faced 2.f4, another bad move, committing too early.  See the following 27-move demolition, noting that I use his early commitment of weaking e4 to do things like create posts on squares like f5 (note how long that Knight sits on f5 hitting critical squares and weaknesses, like e3.

Black should have no issues at all after 1.d4 d5 2.e3?

2...Nf6 develops a piece to a perfectly logical square. White has played the pretty innocuous 2.e3. Black can't be worse.

Thanks for the replies!  I've played a lot of chess games but have only recently begun to try to take my game further with such theory :)

Just starting out playing the 1.d4 d5 and 1.e4 e5 games is the right thing to do. Don't worry about all the popular Grunfeld - Sicilian etc etc for a good while