The reti opening is when white plays 1. Nf3. The Reti gambit is my favourite. Here is what happens.
Reti

1. Nf3 is not the Reti opening. 1. Nf3 d5 2. c4 is the Reti opening.
chessvids is right, it needs to be 1.Nf3 d5 2.c4 to be an official Reti.

To be a Reti, one needs to play Nf3 ...d5 c4, AND unless black plays ...dxc4 or ...d4, but plays ..c6 or ...e6, etc, white plays b3 instead of transposing into a QG

When you hear someone doing a Reti, they are actually referring to an ancient dance where you sing about the blessings around a fire wearing a headdress resembling a serpent and dance for your god Quetzalcoatl.
Or in some cases you see someone dancing badly, you can roll your eyes and say, "Yep, he is definately doing a Reti."

Reti's Opening refers to the narrow group of variations resulting from 1 Nf3 d5 2 c4 which do not transpose into other variations...
No, it is a not an opening please don't try to look like you know stuff. Here is a quote from wikipedia (please don't try and discredit wiki if you have a problem with being wrong)
Because the single opening move 1.Nf3 is rife with transpositional possibilities, it is incorrect to infer that any chess game opening with that move is an example of the Réti Opening. For example, 1.Nf3 d5 2.c4 e6 3.d4 Nf6 4.Nc3 is the Queen's Gambit Declined. The Réti should not be thought of as a single opening sequence, and certainly not a single opening move, but as an opening complex with many variations sharing common themes.

Reti's Opening refers to the narrow group of variations resulting from 1 Nf3 d5 2 c4 which do not transpose into other variations...
No, it is a not an opening please don't try to look like you know stuff. Here is a quote from wikipedia (please don't try and discredit wiki if you have a problem with being wrong)
Because the single opening move 1.Nf3 is rife with transpositional possibilities, it is incorrect to infer that any chess game opening with that move is an example of the Réti Opening. For example, 1.Nf3 d5 2.c4 e6 3.d4 Nf6 4.Nc3 is the Queen's Gambit Declined. The Réti should not be thought of as a single opening sequence, and certainly not a single opening move, but as an opening complex with many variations sharing common themes.
a lot of openings can transpose to other openings, but as of 1.Nf3 d5 2.c4 its the reti. just because it can change doesnt mean that doesnt make it a reti.. (and most of the time it will change to something else)

It could be that when someone said "doing a Reti" that they were referring to a famous maneuver which he used in his opening where he Fianchettos his Queen Bishop to b2 and then maneuvers his queen to a1 creating a battery shooting down the diagonal. This was a very cool maneuver, and it's what I think of when I think of a "Reti Maneuver".
Check out:
http://www.chessgames.com/perl/chessgame?gid=1102115
and:
http://www.chessgames.com/perl/chessgame?gid=1007029

Anyone who uses wikipedia as their primary source shouldn't be accusing anyone else of ignorance.

The Reti is an opening, but also a system because there are many different lines in it, just like you would see in the Ruy Lopez or Sicilian. There aren't many lines in the Orangutan, which is why you don't call it the Orangutan system.
I love the Reti Opening, because I like to play Nf3/Nf6 on my first move no matter what the opponent plays. 1. Nf3 is not Reti, but you can pretty much play 2. c4 no matter what black plays.
1. Nf3 d5 2. c4 is the sexiest opening to me. Reti Gambit accepted are such exciting games, aren't they?
I read the article about Mr Reti, but in chess, what does "doing a reti" mean and what is a reti in an opening game?
Best regards,
Inu